CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 7 - MCQExams.com

Equation of the circle of radius 5 whose centre lies on y-axis in first quadrant and passes through$$\left( {3,\,\,\,\,2} \right)$$ is 
  • $${x^2} + {y^2} - 12y + 11 = 0$$
  • $${x^2} + {y^2} - 6y - 1 = 0$$
  • $${x^2} + {y^2} - 8y + 3 = 0$$
  • None of these
A circle is concentric with circle $$x^{2}+ y^{2}-2x+4y-20=0$$. If perimeter of the semicircle is $$36$$ then the equation of the circle is :
  • $$x^{2}+y^{2}-2x-4y-44=0$$
  • $$(x-1) ^{2}+(y+2) ^{2}=(126/11) ^{2}$$
  • $$x^{2}+y^{2}-2x+4y-43=0$$
  • $$none\ of\ these$$
The axes are translated so that the new equation of the circle $$x^{2}+y^{2}-5x+2y-5=0$$ has no first degree terms. Then the new equation is
  • $$x^{2}+y^{2}=9$$
  • $$x^{2}+y^{2}=\dfrac {49}{4}$$
  • $$x^{2}+y^{2}=\dfrac {81}{16}$$
  • $$none\ of\ these$$
vertices of an ellipse are $$(0,\pm 10)$$ and its eccentricity $$e=4/5$$ then its equation is 
  • $$90x^2-40y^2=3600$$
  • $$80x^2+50y^2=4000$$
  • $$36x^2+100y^2=3600$$
  • $$100x^2+36y^2=3600$$
The name of the conic represent by the equation $$x^2+y^2-2y+20x+10=0$$ is
  • a hyperbola
  • an ellipse
  • a parabola
  • circle
The equation of the circle passing through the foci of the ellipes  $${\frac{x}{{16}}^2} + {\frac{y}{{{9^{}}}}^2} = 1$$ and having centre at $$\left( {0,3} \right)$$ is 

  • $${x^2} + {y^2} - 6y - 7 = 0$$
  • $${x^2} + {y^2} - 6y +7 = 0$$
  • $${x^2} + {y^2} - 6y - 5 = 0$$
  • $${x^2} + {y^2} - 6y + 5 = 0$$
The equation of ellipse whose major axis is along the direction of x-axis, eccentricity is $$e=2/3$$
  • $$36x^2+20y^2=405$$
  • $$20x^2+36y^2=405$$
  • $$30x^2+22y^2=411$$
  • $$22x^2+32y^2=409$$
The equation $$\dfrac { x ^ { 2 } } { 10 - a } + \dfrac { y ^ { 2 } } { 4 - a } = 1$$ represents an ellipse if
  • $$a < 4$$
  • $$a > 4$$
  • $$4 < a < 10$$
  • None of these
Eccentricity of the hyperbola $$x^{2}-y^{2}=4$$ is 
  • $$2$$
  • $$1$$
  • $$\dfrac {3}{2}$$
  • $$\sqrt {2}$$
If the latus rectum of an ellipse $$x ^ { 2 } \tan ^ { 2 } \varphi + y ^ { 2 } \sec ^ { 2 } \varphi =$$ $$1$$ is $$1 / 2 $$ then $$\varphi $$ is
  • $$\pi / 2$$
  • $$\pi / 6$$
  • $$\pi / 3$$
  • $$5$$ $$\pi/ 12$$
If a circle with centre $$(0,0)$$ touches the line $$5x+12y=1$$ then it equation will be
  • $$169(x^{2}+y^{2})=1$$
  • $$ (x^{2}+y^{2})=169$$
  • $$16(x^{2}+y^{2})=1$$
  • $$ (x^{2}+y^{2})=13$$
Consider the set of hydperbola $$xy=k,k\ \in\ R$$. Let $$e_{1}$$ be the eccentricity when $$k=4$$ and $$e_{2}$$ be the eccentricity when $$k=9$$ . Then $$e^{2}_{1}+e^{2}_{2}=$$
  • $$2$$
  • $$3$$
  • $$4$$
  • $$1$$
A circle has its centre on the $$y-axis$$ and passes through the origin, touches another circle with centre $$(2,2)$$ and radius 2, then the radius of the circle is 
  • $$1$$
  • $$1/2$$
  • $$1/3$$
  • $$1/4$$
$$L L ^ { '}$$ is the latus rectum of an ellipse and $$\triangle S ^ { \prime } L L ^ { ' }$$ is an equilateral triangle. Then $$e =$$
  • $$\dfrac { 1 } { \sqrt { 2 } }$$
  • $$\dfrac { 1 } { \sqrt { 3 } }$$
  • $$\dfrac { 1 } { \sqrt { 5 } }$$
  • $$\dfrac { 1 } { \sqrt { 7 } }$$
Length of the latus rectum of the parabola $$\sqrt {x}+\sqrt {y}=\sqrt {a}$$ is
  • $$a\sqrt {2}$$
  • $$\dfrac {a}{\sqrt {2}}$$
  • $$a$$
  • $$2a$$
If there is exactly one tangent at a distance of $$4$$ units from one of the focus of $$\dfrac {x^{2}}{a^{2}}+\dfrac {y^{2}}{a^{2}-16}=1,a > 4$$, the length of latus rectum is :-
  • $$16$$
  • $$\dfrac {8}{3}$$
  • $$12$$
  • $$15$$
The equation $$\dfrac{x^2}{2-r}+\dfrac{y^2}{r-5}+1=0$$ represents an ellipse, if
  • $$r>2$$
  • $$r\in \left(2,\:\dfrac{7}{2}\right)\cup \left(\dfrac{7}{2},5\right)$$
  • $$r>5$$
  • $$r<2$$
A variable circle is drawn to touch the x-axis at the origin.The locus of the pole at the straight line $$6 x + m y + n = 0$$ w.r.t. the variable circle has the equation:-
  • $$x ( m y - n ) - e y ^ { 2 } = 0$$
  • $$x ( m y + n ) - e y ^ { 2 } = 0$$
  • $$x ( m y - n ) + \ell y ^ { 2 } = 0$$
  • none
General solution of the equation $$ y=x\dfrac{dy}{dx}+\dfrac {dx}{dy}$$ represents _____________.
  • a straight line or hyperbola
  • a straight line or parabola
  • a parabola or hyperbola
  • circles
Equation of circles which touch both the axes and whose centres are at a distance of $$2\sqrt {2}$$ units from origin are 
  • $$x^{2}+y^{2}\pm 4x\pm 4y+4=0$$
  • $$x^{2}+y^{2}\pm 2x\pm 2y+4=0$$
  • $$x^{2}+y^{2}\pm x\pm y+4=0$$
  • $$x^{2}+y^{2}-4=0$$
The equation of the circle in the first quadrature touching each coordinate axis at a distance of one unit from the origin 
  • $$x^{2}+y^{2}-2x-2y+1=0$$
  • $$x^{2}+y^{2}-2x-1=0$$
  • $$x^{2}+y^{2}-2x=0$$
  • None of these
The equation of the circle which circumscribes the triangle formed by the lines x + y + 3 = 0, x - y + 1 =0 and x = 3 is 
  • $$x^2+y^2-6x+2y-15=0$$
  • $$3x^2+3y^2-9=0$$
  • $$x^2+y^2+6x-2y+15=0$$
  • None of these
The parametric form of the equation of the circle $${ x }^{ 2 }+{ y }^{ 2 }=9$$ is:
  • $$x=\sqrt { 3 } \cos { \theta } ,$$ $$y=\sqrt { 3 } \sin { \theta } $$
  • $$x=3\cos { \theta } ,\quad y=3\sin { \theta } $$
  • $$x=-\sqrt { 3 } \cos { \theta } ,$$ $$y=-\sqrt { 3 } \sin { \theta } $$
  • none of these
The length of the latus rectum of the parabola $${ 2y }^{ 2 }+3y+4x-2=0$$ is ________.
  • $$\dfrac{ 3 }{ 2 } $$
  • $$\dfrac{ 1 }{ 3 } $$
  • $$2$$
  • None of these.
The equation of a circle with centre at $$(1, -2)$$ and passing through the centre of the given circle $$x^2+y^2+2y-3=0$$, is?
  • $$x^2+y^2-2x+4y+3=0$$
  • $$x^2+y^2-2x+4y-3=0$$
  • $$x^2+y^2+2x-4y-3=0$$
  • $$x^2+y^2+2x-4y+3=0$$
The equation of circle whose centre is $$(1, -3)$$ and which touches the line $$2x-y-4=0$$, is
  • $$5x^2+5y^2+10x+30y+49=0$$
  • $$5x^2+5y^2+10x-30y-49=0$$
  • $$5x^2+5y^2-10x+30y-49=0$$
  • None of these
For the ellipse $$ {12x}^{2} +{4y}^{2} +24x-16y+25=0 $$
  • centre is $$(-1,2) $$
  • Length of axes are $$ {\sqrt {3}} and 1 $$
  • eceentricity is $$ \sqrt {\cfrac {2} {3}} $$
  • All of these
If a conic passing through origin has $$( 3,3 ) , ( - 4,4 )$$ as its focii, then

  • auxillary circle is $$( 2 x + 1 ) ^ { 2 } + ( 2 y - 7 ) ^ { 2 } = 2$$
  • auxillary circle is $$( 2 x + 1 ) ^ { 2 } + ( 2 y - 7 ) ^ { 2 } = 98$$
  • auxillary circle is $$( 2 x + 1 ) ^ { 2 } + ( 2 y - 1 ) ^ { 2 } = 49$$
  • auxillary circle is $$( 2 x + 1 ) ^ { 2 } + ( 2 y - 1 ) ^ { 2 } = 41$$
Equation of the ellipse whose minor axis is equal to the distance between foci and whose latus rectum is $$10 ,$$ is given by ____________.
  • $$2 x ^ { 2 } + 3 y ^ { 2 } = 100$$
  • $$2 x ^ { 2 } + 3 y ^ { 2 } = 80$$
  • $$x ^ { 2 } + 2 y ^ { 2 } = 100$$
  • none of these
The latus rectum of a parabola whose focal chord is $$PSQ$$ such that $$SP=3$$ and $$SQ=2$$, is given by 
  • $$\dfrac{24}{5}$$
  • $$\dfrac{12}{5}$$
  • $$\dfrac{6}{5}$$
  • $$\dfrac{48}{5}$$
The angle between the curves $$x^3-3xy^2=2$$ and $$3x^2y-y^3=2$$ is?
  • $$\dfrac{\pi}{6}$$
  • $$\dfrac{\pi}{4}$$
  • $$\dfrac{\pi}{3}$$
  • $$\dfrac{\pi}{2}$$
The ratio of the ordinates of a point and its corresponding point is $$\frac { 2 \sqrt { 2 } } { 3 }$$ then eccentricity is ____________________.

  • $$\frac { 1 } { 3 }$$
  • $$\frac { 2 } { 3 }$$
  • $$\frac { \sqrt { 2 } } { 3 }$$
  • $$\frac { 2\sqrt { 2 } } { 3 }$$
The length of the latus rectum of the parabola $$4y^{2}+2x-20y+17=0$$ is:
  • $$3$$
  • $$6$$
  • $$\dfrac{1}{2}$$
  • $$9$$
The locus of the moving point $$P(x,y)$$ satisfying $$\sqrt { { \left( { x-1 } \right)  }^{ 2 }+{ y }^{ 2 } } +\sqrt { { \left( { x+1 } \right)  }^{ 2 }+({ y-{ \sqrt { 12 } ) }^{ 2 } } } =$$ a will be an ellipse if 
  • $$a<4$$
  • $$a>2$$
  • $$a>4$$
  • $$a<2$$
A circle has radius $$3$$ units and its centre lies on the line $$y=x-1$$. Then the equation of this circle if it passes through the point $$(7, 3)$$, is?
  • $$x^2+y^2-8x-6y=16$$
  • $$x^2+y^2+8x+6y+16=0$$
  • $$x^2+y^2-8x-6y-16=0$$
  • None of these
$$ABCD$$ is a square with side $$a$$. If $$AB$$ and $$AD$$ are taken as positive coordinate axes then equation of circle circumscribing the square is
  • $$x^{2}+y^{2}-ax-ay=0$$
  • $$x^{2}+y^{2}+ax+ay=0$$
  • $$x^{2}+y^{2}-ax+ay=0$$
  • $$x^{2}+y^{2}+ax-ay=0$$
The latus rectum of the conic $${ 3x }^{ 2 }+{ 4y }^{ 2 }-6x+8y-5=0$$ is ________________________.
  • $$3$$
  • $$\dfrac { \sqrt { 3 } }{ 2 } $$
  • $$\dfrac { 2 }{ \sqrt { 3 } } $$
  • $$\dfrac { 4 }{ \sqrt { 3 } } $$
The circle passing through $$\left(t,1\right),\left(1,t\right)$$ and $$\left(t,t\right)$$ for all values of $$t$$ also passes through 
  • $$\left(0,0\right)$$
  • $$\left(1,1\right)$$
  • $$\left(1,-1\right)$$
  • $$\left(-1,-1\right)$$
The area bounded by the parabola $${ y }^{ 2 }=4xy\quad $$ and its rectum is :-
  • $$\frac { { 4 }^{ a } }{ 3 } sq-units$$
  • $$\frac { { 8a }^{ 2 } }{ 3 } sq-units$$
  • $$\frac { { 4a }\sqrt { a } }{ 3 } sq-units$$
  • $$\frac { { 8a }\sqrt { a } }{ 3 } sq-units$$
Identify the types of cuves with represent by the equation $$\frac { { x }^{ 2 } }{ 1-r } -\frac { { y }^{ 2 } }{ 1+t } =1 $$, where $$r>1$$
is _______________.
  • An ellipse
  • A hyperbola
  • A circle
  • None of these
The equation of the circle which passes through the point (3,-2) and (-2,0) and centre line 2x-y=3,is 
  • $${ x }^{ 2 }+{ y }^{ 2 }-3x-12y+2=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-3x+12y+2=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+3x+12y+2=0$$
  • None of these
The eq. of the circle which touches the exes of y at a distance of $$4$$ from the origin and cuts the intercepts of $$6$$ units from the axis of x is
  • $$x^2 +y^2 \pm 10x \pm 8y + 16=0$$
  • $$x^2 +y^2 \pm 5x \pm 4y + 16=0$$
  • $$x^2 +y^2 \pm 10x \pm 8y - 16=0$$
  • $$x^2 +y^2 \pm 5x \pm 4y - 16=0$$
Let $$P,\ Q,\ R,\ S$$ be the feet of perpendicular drawn from the point $$(1,\ 1)$$ the lines $$y=3x+4$$ and $$y=-3x+6$$ and their angle bisectors respectively, the equation of the circle whose extremities of a diameter are $$R$$ and $$S$$ is 
  • $$3x^{2}+3y^{2}+104x-110=0$$
  • $$x^{2}+y^{2}+104x-110=0$$
  • $$3x^{2}+3y^{2}-4x-18y+16=0$$
  • $$x^{2}+y^{2}-4x-18+16=0$$
The length of the latus rectum of the parabola whose focus is (3,0) and directrix is 3x-4y-2=0 is
  • 12
  • 1
  • 4
  • none of these
A parabola passing through the point $$(-4,-2)$$ has its vertex at the origin and $$y-$$axis as its axis. The latus rectum of the parabola is
  • $$6$$
  • $$8$$
  • $$10$$
  • $$12$$
The equation of the latusrectum of the parabola $${ x }^{ 2 }+4x+2y=0$$ is:-
  • 3y-2=0
  • 3Y+2=0
  • 2Y-3=0
  • 2Y+3=0
The circle $$(x-3a)^{2}+y^{2}=8ax$$ intersects the parabola $$y^{2}=4ax$$ at the ends of the rectum of the parabola. 
  • True
  • False
The equation of the circle having as a diameter, the chord $$x - y - 1 = 0$$ of the circle $$2x^2 + 2y^2 - 2x - 6y - 25 = 0$$, is
  • $$x^2 + y^2 - 3x - y - \dfrac{29}{2} = 0$$
  • $$2x^2 + 2y^2 + 2x - 5y - \dfrac{29}{2} = 0$$
  • $$2x^2 + 2y^2 - 6x - 2y - 21 = 0$$
  • None of these
Equation of the circle which is such that the length of the tangents to it from the points (1,0), (0, 2) and (3, 2) are $$1,\sqrt { 7 } $$ respectively is
  • $$6({ x }^{ 2 }+{ y }^{ 2 })-28x-5y+28=0$$
  • $$9({ x }^{ 2 }+{ y }^{ 2 })-28x-5y+28=0$$
  • $$3({ x }^{ 2 }+{ y }^{ 2 })-28x-5y+28=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-28x-5y+28=0$$
The curve represented by $$Rs \left(\dfrac{1}{z}\right)=C$$ is (where $$C$$ is a constant and $$\neq 0$$)
  • Ellipse
  • Parabola
  • Circle
  • Straight line
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