Tangents And Its Equations - Class 11 Commerce Applied Mathematics - Extra Questions
Find the equation of the normal to the parabola y2=4x, which is (i) parallel to the line y=2x−5, (ii) perpendicular to the line x+3y+1=0.
Find the equation of tangents to the curve y=cosx,x∈[−2π,2π] , which passes through (0,1)
The perpendicular from the origin to then line y=mx+c meets it at the point (−1,2). Find the values of m & c.
Find the equations of the tangent and the normal to the following curves. x2+y2+xy=3atP(1,1)
Find the equation of the normal to the curve y=4x3−3x+5 which are perpendicular to the line 9x−y+5=0.
Find the equation of tangent to the curve y=x2+4x+1 at (−1,−2).
x2=4y : Find the equation of tangent passing through (-1,2)
Find the equation of the tangent and the normal to the following curve at the indicated point. y2=4ax at (x1,y1).
Find the equation of the tangent and the normal to the following curve at the indicated point. x=at2, y=2at at t=1.
Find the equation of the tangent to the curve √x+√y=a at the point (a24,a24).
Find the equation of the tangent and the normal to the following curve at the indicated point. xy=c2 at (ct,ct).
Find the equation of the tangent and the normal to the following curve at the indicated point. y=x2 at (0,0).
Find the equation of the normal to y=2x3−x2+3 at (1,4).
Find the equation of the tangent and the normal to the following curve at the indicated point. x2a2−y2b2=1 at (√2a,b).
If the tangent to a curve at a point (x,y) is equally inclined to the coordinate axes, then write the value of dydx.
Find the equation of the tangent and the normal to the following curve at the indicated point. x=asect,y=btant at t.
Find the equation of the tangent to the curve y=−5x2+6x+7 at the point (12,354).
Find the equation of the normal to the curve y=2x2+3sinx at x=0.
Find the equation of the tangent and the normal to the given curve at the indicated point: y=cot2x−2cotx+2atx=π4
Find the equation of all lines having slope -1 that are tangents to the curve y=1x−1,x≠1.
Find the equations of all lines having slope 0 which are tangent to the curve y=1x2−2x+3.
Find the equation of all lines having slope 2 which are tangents to the curve y=1x−3,x≠3.
Find the equations of the tangent and normal to the given curves at the indicated points: (i) y=x4−6x3+13x2−10x+5 at (0,5). (ii) y=x4−6x3+13x2−10x+5 at (1,3) (iii) y=x3 at (1,1) (iv) y=x2 at (0,0) (v) x=cost,y=sint at t=π4
Find the equations of the tangent and normal to the given curve at the indicated point:
y=x4−6x3+13x2−10x+5 at (1,3)
Find the equation of the tangent line to the curve y=x2−2x+7 which is. (a) parallel to the line 2x−y+9=0. (b) perpendicular to the line 5y−15x=13.
Find the equation of the tangent to the curve y=√3x−2 which is parallel to the line 4x−2y+5=0
Find the equation of the normal to the curve y=x3+2x+6 which are parallel to the line x+14y+4=0.
Find the equation of the tangent line to the curve y=x2−2x+7 which is perpendicular to the line 5y−15x=13.
Find the equations of the tangent and normal to the given curve at the indicated point:
y=x2 at (0,0).
Find the equation of the normal at the point (am2,am3 ) for the curve ay2=x3 .
Find the points on the curve y=x3−2x2−x at which the tangent lines are parallel to the line y=3x−2.
Find a point on the curve y=x3−3x where the tangent is parallel to the chord joining (1,−2) and (2,2).
Find the pair of tangents from the origin to the circle x2+y2+2gx+2fy+c=0 and hence condition for these tangents to be perpendicular.
Find the equation of tangent and normal to the curve x=sin3t, y=cos2t at t=π4.
Find the equation of normals to the curve y=x3+2x+6 which are parallel to the line x+14y+4=0
The line to the normal of the curve xy=1 is ?
Find the equation of tangents to the curve y=cosx, that are parallel to the line x+2y=0
Find the equation of the normal to the curve y2=ax3at(a,a)
Find the equation of the tangent to the curve y=3x2−x+1 at P(1,3).
Find the equation of the tangent(s) to the following graphs at the points(s) whose x or y- coordinates is given: y=x2−2, where y=−2
Find the equation of the normal to the curve y=4x3−3x+5 which are perpendicular to the line 9x−y+5=0
Find the equation of the tangent(s) to the following graphs at the points(s) whose x or y- coordinates is given y=x2 where x=2
Find the equation of the normal to the circle x2+y2=5 at the point (1,2).
Find the equation of tangent & normal to curve 2x3+2y3−9xy=0 at the point (2,1)
Find the equation of the tangent(s) to the following graphs at the points(s) whose x or y- coordinates is given: y=x2+2 where x=−1
Find the equation of the tangent to the curve y=x2−2 at y=−1
Find the equation of the normal to the curve y=√6x+3 at the point for which x=13.
A curve has equation y=x(x−a)(x+a),where a is a constant. Find the equations of the tangents to the graph at the points where it crosses the x-axis.
Equation of the normal line to y=logx at the point at which the curve crosses x−axis is
Show that the equation of normal at any point on the curve x=3cost−cos3t, y=3sint−sin3t is 4(ycos3t−xsin3t)=3sin4t.
If the line joining the points (0,3) and (5,−2) is a tangent to the curve y=cx+1, then the value of c is ?
Find the equation of the normal to the curve x2=4y which passes through the point (1,2)
Find the equations of tangent and normal to the curves at the indicated points on it. (i) y=x2+4x+1 at (−1,−2) (ii) 2x2+3y2−5=0 at (1,1) (iii)x=acos3θ,y=asin3θ at θ=π4
The equation of tangent at (5,3) for the curve x2−y2=16
The tangent at (4,6) to the curve y2=9x
The equation of tangent at (1,2) on the curve x2=2y
Show that the equation of normal at any point on the curve x=3cosθ−cos3θ,y=3sinθ−sin3θ is 4(ycos3θ−xsin3θ)=3sin4θ.
Find the equations of the tangent and the normal to the curve y=x−7(x−2)(x−3) at the point where it cuts the x-axis.
Find the points on the curve x24+y225=1 at which the tangents are parallel to the y-axis.
Find the equation of the tangent and the normal to the following curve at the indicated point. y2=x34−x at (2,−2).
Find the equation of the tangent and the normal to the following curve at the indicated point. y=2x2−3x−1 at (1,−2).
Find the equation of the tangent and the normal to the following curve at the indicated point. c2(x2+y2)=x2y2 at (xcosθ,csinθ).
Find the equation of the tangent and the normal to the following curve at the indicated point. x2a2−y2b2=1 at (x0,y0).
Find the equation of the tangent and the normal to the following curve at the indicated point. y=x2+4x+1 at x=3.
Find the equation of the tangent and the normal to the following curve at the indicated point. y2=4ax at (am2,2am)
Determine the equation(s) of tangent(s) line to the curve y=4x3−3x+5 which are perpendicular to the line 9y+x+3=0.
Find the equation of the tangent line to the curve y=x2+4x−16 which is parallel to the line 3x−y+1=0.
Find the equation of the tangent and the normal to the following curve at the indicated point. x=2at21+t2,y=2at31+t2 at t=1/2.
Find the equation of the tangent and the normal to the following curve at the indicated point. x2=4y at (2,1).
Find the equation of the tangent and the normal to the following curve at the indicated point. x=3cosθ−cos3θ,y=3sinθ−sin3θ.
Find the equation of the tangent and the normal to the following curve at the indicated point. 4x2+9y2=36 at (3cosθ,2sinθ).
Find the equation of the tangent and the normal to the following curve at the indicated point. x=a(θ+sinθ),y=a(1−cosθ) at θ.
Find an equation of normal line to the curve y=x3+2x+6 which is parallel to the line x+14y+4=0.
Find the equation of the normal to the curve ay2=x3 at the point (am2,am3).
Find the equation of the tangent and the normal to the following curve at the indicated point. x=θ+sinθ,y=1+cosθ at θ=π2.
Find the equation of the tangent line to the curve y=x2−2x+7 which is perpendicular to the line 5y−15x=13.
Find the equation of the tangent to the curve y=√3x−2 which is parallel to the line 4x−2y+5=0.
At what points will be tangents to the curve y=2x3−15x2+36x−21 be parallel to x-axis? Also, find the equations of the tangents to the curve at these points.
Find the equation of the tangent to the curve x=sin3t,y=cos2t at t=π4.
Find the equation of the tangents to the curve 3x2−y2=8, which passes through the point (43,0).
Find the equation of the tangent to the curve x2+3y−3=0, which is parallel to the line y=4x−5.
Write the equation of the tangent drawn to the curve y=sinx at the point (0,0).
Write the equation of the normal to the curve y=cosx at (0,1).
Write the equation of the normal to the curve y=x+sinxcosx at x=π2.
Write the equation of the tangent to the curve y=x2−x+2 at the point where it crosses the y-axis.
Find the points on the curve y=x3−3x, where the tangent to the curve is parallel to the chord joining (1,−2) and (2,2).
Find the equation of the tangent and the normal to the given curve at the indicated point: x2a2−y2b2=1 at (asecθ,btanθ)
Find the equation of the tangent and the normal to the given curve at the indicated point: y2=4ax at (am2,2am)
Find the equation of the tangent and the normal to the given curve at the indicated point: y2=4ax at (at2,2at)
Find the equation of the tangent and the normal to the given curve at the indicated point: y=x2−2x+7 at (1,6)
Find the equation of the tangent and the normal to the given curve at the indicated point: y=x3 at P(1,1)
Find the equation of the tangent and the normal to the given curve at the indicated point: x2a2+y2b2=1 at (acosθ,bsinθ)
Find the equation of the tangent and the normal to the given curve at the indicated point: 16x2+9y2=144 at (2,y1), where y1>0
Find the equation of the normal to the curve y=(sin2x+cotx+2)2 at x=π2
Find the equation of the tangent to the curve √x+√y=a at (a24,a24)
Find the equation of the tangent to the curve y=(sec4x−tan4x) at x=π3
Find the equation of the tangent to the curve x2+3y=3, which is parallel to the line y−4x+5=0.,
Show that the tangent to the curve y=2x3−4 at the points x=2 and x=−2 are parallel.
Show that the equation of the tangent to the hyperbola x2a2−y2b2=1 at (x1,y1) is xx1a2−yy1b2=1
Find the equation of the tangent to the curve x2+2y=8, which is perpendicular to the line x−2y+1=0
Find the equation of the tangent at t=π4 for the curve x=sin3t,y=cos2t
Prove that the equation of the normal to x2/3+y2/3=a2/3 is ycosθ−xsinθ=acos2θ,where θ is the angle which the normal makes with axis of x.
Find the equation of the tangent to the curve 2x2+3y2=14, parallel to the line x+3y=4.
Find the equation of tangent to the curve x=(θ+sinθ),y=(1+cosθ) at θ=π4
If the curve C in the xy place has the equation x2+xy+y2=1, then the fourth power of the greatest distance of a point on C from the origin, is
Find the equation of the normal to the curve y=(1+x)y+sin−1(sin2x) at x=0.
Find the equation of tangent to the curve y=√3x−2, which is parallel to the line 4x−2y+5=0.
Find the equation of the normal at the point (am2,am3) for the curve ay2=x3.
Find the equation of all the tangents to the curve y=cos(x+y),−2π≤x≤2π that are parallel to the line x+2y=0.
Find the equations of tangents to the curve 3x2−y2=8, which pass through the point (43,0)
Find the equation of tangent to the curve x=sin3t,y=cos2t at t=π4.
Find the equation of tangent and normals to the following curves at the indicated points on them : y=x2+2ex2 at (0,4)
The equation of normal to the curve y=tanxat(0,0) is _______.
Find the equation of tangent and normals to the following curves at the indicated points on them : xsin2y=ycos2x at (π4,π2)
Find the equation of tangent and normals to the following curves at the indicated points on them : 2xy+πsiny=2π at (1,π2)
Find the equation of tangent and normals to the following curves at the indicated points on them : x2−√3xy+2y2=5at(√3,2)
Find the equation of tangent and normals to the following curves at the indicated points on them : x3+y3−9xy=0 at (2,4)
Find the equation of tangent to the curve x2+y2−2x−4y+1−0 which a parallel to the X−axis.
Find the equation of tangent and normals to the following curves at the indicated points on them : x=sinθ and y=cos2θ at θ=π6
Find the equation of tangent and normals to the following curves at the indicated points on them : x=√t,y=t−1√t at =4
Solve the following: Find the equation of the tangent and normal drawn to the curve y4−4x2−6xy=0 at the point M(1,2).
Find the equation of all lines having slope -1 that are tangents o the curve y=1x−1,x≠3
Find the equal of the normal to curve y2=4x which passes through the point (1,2).
Find the equations of the tangent line to the curve y=x2−2x+7 which is parallel to the line 2x−y+9=0
Find the equations of all lines having slope 0 which are tangent to the curve y=1x2−2x+3
Find the equations of the tangents and normal to the given curves at the indicated points : y=x3 at (1,1)
Find the equations of the tangents and normal to the given curves at the indicated points : y=x4−6x3+13x2−10x+5at (1,3)
Find the equations of the tangents and normal to the given curves at the indicated points : y=x4−6x3+13x2−10x+5at (0,5)
Find the equations of the tangents and normal to the given curves at the indicated points : y=x2 at (0,0)
Find the equation of the tangents and normal to the parallel y2=4axat the point (at2,2at)
Find the equation of the normal at the point (am2,am3) for the curve ay2=x3
Find the equation of the normal to the curve y=x3+2x+6 which are parallel to the line x+14y+4=0
Find the equations of the tangent line to the curve y=x2−2x+7 which is parallel to the line 5y−15x=13
Find the equations of the tangents and normal to the hyperbola x2a2−y2b2=1 at the point (x_{0},y_{0})$$
Find the equation of the tangents to the curve y=√3x−2 which is parallel to the line 4x−2y+5=0
Find the equation of all lines having slope 2 which are tangents to the curve y=1x−3,x≠3
For curves y=sin2X, find equation of normal at (π3,34).
Find equation of tangent and normal following curves, at given points. (c) xy=a2, at (at,at)
Find equation of tangent and normal following curves, at given points. (b) y2=4ax, at x=a
Find equation of tangent and normal following curves, at given points. (f) y=2x2−3x−1, at (1,−2)
Find all equations of lines which are tangent to the curve y+2x−3=0 and slope of those is 2.
Find equation of tangent and normal following curves, at given points. (a) y=x2+4x+1, at x=3
Find equation of tangent and normal following curves, at given points. (d) y2=4ax, at (am2,2am)
Find equation of tangent and normal following curves, at given points. (g) x=at2,y=2at,t=1
For curve x−asin3t,y=bcos3t find equation n of tangent at t=π2
Find equation of tangent and normal following curves, at given points. (h) x=θ+sinθ,y−1−cosθ at 0=π2
For the curve y=4x3−2x5, find all the points at which the tangents passes through the origin.
Let tangent at a point P on the curve x2myn2=a4m+n2 meets the x-axis and y-axis at A and B respectively if AP : PB is nλm where P lies between A and B then find the value of λ.
Construct the graph of the function y = (x2 + x) (x - 2). Write the equation of the tangent to the graph at the point with abscissa x0 =Find the coordinates of the points of intersection of the tangent and the graph of the function.
Find the equations of the tangent and normal to the curve x=asin3θ and y=acos3θ at θ=π4.
Find the equation of the tangent and normal to the parabola x2−4x−8y+12=0 at (4,32).
Find the equation of the normal to the curve y=(1+x)+(sin2x) at x=0.
To find the equation of tangent and normal to the circle x2+y2−3x+4y−31=0 at the point (2,3).
Find the equation of tangent and normal to the curve at the indicated points on it y=x2+4x+1 at (−1,−2)
If the tangent at (x1y1) to the curve x3+y3=a3 meets the curve again in (x2,y2), then prove that x2x1+y2y1=−1 .
The point A(2,2) lies on the curve y=x2−2x+2. The normal to the curve at A intersects the curve again at B. Find the coordinate of B.
If |f(x1)−f(x2)|<(x1−x2)2 for all x1,x2ϵR. Find the equation of tangent of tangent to the curve y= f(x) at the point(1, 2)
Find equation of tangent and normal following curves, at given points. (e) x2a2−y2b2=1, at (a sec 0, b tan 0)
Class 11 Commerce Applied Mathematics Extra Questions