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CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 12 - MCQExams.com

The latus rectum of parabola y2=5x+4y+1 is
  • 10
  • 5
  • 54
  • 52
A circle touch the line L and the circle C1 externally such that both the circles are on the same side of the line, then the locus of center of the circle is
  • ellipse
  • hyperbola
  • parabola
  • parts of straight line
The equations x=t4,y=t24 represents 
  • An ellipse
  • A parabola
  • A circle
  • A hyperbola
Length of the latus rectum of the hyperbola xy=c2, is
  • 2c
  • 2c
  • 22c
  • 4c
Lissajous figure obtained by combining x=ASin ωt and y=ASin (ωt+Π/4) will be 
  • an ellipse
  • a straight line
  • a circle
  • a parabola
Let PQ be a variable focal chord of the parabola y2=4ax(a>0) whose vertex is A. then the locus of centroid of ΔAPQ lies on a parabola whose length of latusrectum is 
  • 2a3
  • a
  • 4a3
  • 5a3
Vertex of the parabola 2y2+3y+4x1=0 is
  • (2532,74)
  • (2532,34)
  • (1532,74)
  • (1732,34)
A circle passes through A(1,2) and the equations of the normal to the circle is x+2y=5. If the circle passes through B(5,5), then the radius of the circle is
  • 32
  • 52
  • 352
  • 52
If the radius of the circle x2+y2+2gx+2fy+c=0 be r, then it will touch both the axes, if 
  • g=f=c
  • g=f=c=r
  • g=f=c=r
  • g=f and c2=r
If two distinct chords of a parabola y2=4ax passing through the point (a,2a) are bisected by the line x+y=1, then the length of the latus rectum can be
  • (2,6)
  • (1,4)
  • (0,2)
  • (0,4)
The equations x=t4,y=t24 represents
  • An ellipse
  • A parabola
  • A circle
  • A hyperbola
If the radius of the circle x2+y2 - 18 x - 12 y + k = 0 be 11 then k =
  • 347
  • 4
  • -4
  • 97
The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by
  • 24/5
  • 12/5
  • 6/5
  • 23/5
If (3x4y1)2100(4x+3y1)2225=1, then
length latusrectum of hyperbola is-

  • 92
  • 403
  • 9
  • 83
If  y22x2y+5=0  is
  • a circle with centre (1,1)
  • a parabola with vertex
  • a parabola with directrix x=3/2
  • a parabola with directrix
The value of α for which three distinct chords drawn from (α,0) to the ellipse x2+2y2=1 are bisected by the parabola y2=4x is 
  • 9
  • 17
  • 8
  • None of these.
The equation x210a+y24a=1 , represents an ellipse , if 
  • a<4
  • a>4
  • 4<a<10
  • a>10
Let PQ be the latus rectum of the parabola y2=4x with vertex A. Minimum length of the projection of PQ on a tangent drawn in portion of parabola PAQ is :
  • 2
  • 4
  • 23
  • 22
C:x216+y212=1 
The equation of parabolas with same latus- rectum as conic C, is/are
  • y25x+3=0
  • y2+6x21=0
  • y26x21=0
  • y2+6x+3=0
The distance between the foci or a hyperbola is double the distance between its vertices and the length of a conjugate axis isThe equation of the hyperbola referred to its axes as axes of coordinates is
  • 3x2y2=3
  • x23y2=3
  • 3x2y2=9
  • x23y2=9
The equation of directrix of a parabola is 3x + 4y + 15 =0 and equation of tangent at vertex is 3x + 4y - 5=Then the length of latus recturn is equal to 
  • 15
  • 14
  • 13
  • 16
Length of the latus rectum of the parabola 25[(x2)2+(y3)2]=(3x4y+7)2 is 
  • 4
  • 2
  • 1/5
  • 2/5
equation of latus rectum of the parabola y216x6y+1=0 is
  • x-7=0
  • x+7=0
  • 2x-7=0
  • 2x+7=0
The latus rectum of a parabola whose directrix is x + y- 2 =0 and focus is (3, -4) is 
  • 32
  • 32
  • 22
  • 32
The y-axis is the directrix of the ellipse with eccentricity e=1/2 and the corresponding focus is at (3, 0), equation to its auxilary circle is
  • x2+y28x+12=0
  • x2+y28x12=0
  • x2+y28x+9=0
  • x2+y2=4
If e,e' be the eccentricities of two conics S and S' and if e2+e,2=3, then bothe S and S'
  • Ellipses
  • Parabola
  • Hyperbola
  • None of these
The equation of circle with centre (1, 2) and tangent x+y5=0 is
  • x2+y2+2x4y+6=0
  • x2+y22x4y+3=0
  • x2+y22x+4y+8=0
  • x2+y22x4y+8=0
The equation of the ellipse with axes along the x-axis and the y-axis, which passes through the points P(4, 3) and Q (6, 2) is
  • x250+y213=1
  • x252+y213=1
  • x213+y252=1
  • x252+y217=1
If the circle describe on the line joining the points (0, 1) and (α,β) as diameter cuts the x-axis in points whose abscissae are roots of equation x2x+3=0 the (α,β)
  • (1, 3)
  • (1, 5)
  • (-5, 1)
  • (-5, -1)
The equation of a circle with origin as a centre and passing through equilateral whose median is of length 3a is
  • x2+y2=9a2
  • x2+y2=16a2
  • x2+y2=a2
  • None of these
If the parabola y2=4ax passes through (2,6) then the equation of the latusrectum is 
  • 2x -9 = 0
  • 4x + 9 = 0
  • 2x + 9 = 0
  • 4x - 9 = 0
The length of the latus rectum of the parabola  4y2+2x20y+17=0  is
  • 3
  • 6
  • 1/2
  • None
The length of the latus rectum of the parabola y24x+4y+8=0is
  • 8
  • 6
  • 4
  • 2
The equation  x212a+y24a=1 represent an ellipse, if:
  • a<12
  • a<4
  • a>12
  • a>4
The equation of circles passing through (3,-6) touching both the axes is 
  • x2+y26x+6y+9=0
  • x2+y2+6x6y+9=0
  • x2+y230x30y+225=0
  • x2+y230x+30y+225=0
If ab the parametric equations x=a(cosΘ+sinΘ),y=b(cosΘsinΘ) represents
  • Hyperbola
  • A circle
  • An ellipse
  • A pair of straight lines
  • A parabola
A common tangent to the conics x2=6y and 2x24y2=9, is __________.
  • x+y=1
  • xy=1
  • x+y=92
  • xy=32
The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by 
  • 24/5
  • 12/5
  • 6/5
  • none of these
The eccentricity of  the hyperbola x23y2+1=0  is 
  • 12
  • 1
  • 2
  • 3
If 5x+9=0 is the directrix of the hyperbola 16x29y2=144, then its correponding focus is:
  • (53,0)
  • (5,0)
  • (5,0)
  • (53,0)
If the centroid of an equilateral triangle is (1,1) and one of its vertices is (-1,2) then, equation of its circum circle is 
  • x^{2}+y^{2}-2x-2y-3=0
  • x^{2}+y^{2}+2x-2y-3=0
  • x^{2}+y^{2}-4x-6y+9=0
  • x^{2}+y^{2}+x-y+5=0
The eccentricity of an ellipse, with its centre at the origin, is\frac{1}{2}. If one of the directrices is x = 4, then the equation of the ellipse is
  • 3x^2 + 4y^2 = 1
  • 3x^2 + 4y^2 = 12
  • 4x^2 + 3y^2 = 12
  • 4x^2 + 3y^2 = 1
Angle between the parabola y^{2} = 4b(x - 2a + b) and x^{2} + 4a(y - 2b - a) = 0 at the common end of their latus rectum, is
  • \tan^{-1}(1)
  • \cot^{-1}1 + \cot^{-1}\dfrac {1}{2} + \cot^{-1} \dfrac {1}{3}
  • \tan^{-1} (\sqrt {3})
  • \tan^{-1} (2) +\tan^{-1} (3)
Equation of a circle whose centre is in I quadrant as \left(\alpha,\ \beta\right) and touches x-axis will be:
  • x^{2}+y^{2}-2\alpha x - 2\beta y + \alpha ^{2}
  • x^{2}+y^{2}+2\alpha x - 2\beta y + \alpha ^{2}
  • x^{2}+y^{2}-2\alpha x + 2\beta y + \alpha ^{2}
  • x^{2}+y^{2} + 2\alpha x + 2\beta y + \alpha ^{2}
0:0:3


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