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

The latus rectum of parabola $${ y }^{ 2 }=5x+4y+1$$ is
  • 10
  • 5
  • $$\dfrac { 5 }{ 4 } $$
  • $$\dfrac { 5 }{ 2 } $$
A circle touch the line L and the circle $${ C }_{ 1 }$$ 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 $$x=\dfrac{t}{4}, y=\dfrac{t^2}{4}$$ represents 
  • An ellipse
  • A parabola
  • A circle
  • A hyperbola
Length of the latus rectum of the hyperbola $$ x y=c^{2},  $$ is
  • $$\sqrt{2} {c}$$
  • $$2c$$
  • $$2\sqrt{2}{c}$$
  • $$4c$$
Lissajous figure obtained by combining x=ASin $$\omega t$$ and y=ASin $$(\omega t+\Pi /4)$$ will be 
  • an ellipse
  • a straight line
  • a circle
  • a parabola
Let $$PQ$$ be a variable focal chord of the parabola $${y^2} = 4ax\left( {a > 0} \right)$$ whose vertex is A. then the locus of centroid of $$\Delta APQ$$ lies on a parabola whose length of latusrectum is 
  • $$\frac{{2a}}{3}$$
  • a
  • $$\frac{{4a}}{3}$$
  • $$\frac{{5a}}{3}$$
Vertex of the parabola $$2{ y }^{ 2 }+3y+4x-1=0$$ is
  • $$\left( \dfrac { 25 }{ 32 } ,\dfrac { -7 }{ 4 } \right) $$
  • $$\left( \dfrac { 25 }{ 32 } ,\dfrac { -3 }{ 4 } \right) $$
  • $$\left( \dfrac { 15 }{ 32 } ,\dfrac { 7 }{ 4 } \right) $$
  • $$\left( \dfrac { 17 }{ 32 } ,\dfrac { -3 }{ 4 } \right) $$
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
  • $$\dfrac {3}{2}$$
  • $$\dfrac {\sqrt {5}}{2}$$
  • $$\dfrac {3\sqrt {5}}{2}$$
  • $$\dfrac {5}{2}$$
If the radius of the circle $${x}^{2}+{y}^{2}+2gx+2fy+c=0$$ be $$r$$, then it will touch both the axes, if 
  • $$g=f=c$$
  • $$g=f=c=r$$
  • $$g=f=\sqrt{c}=r$$
  • $$g=f$$ and $${c}^{2}=r$$
If two distinct chords of a parabola $$y^2 = 4 \,ax$$ 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 $$x=\frac{t}{4},y=\frac{t^2}{4}$$ represents
  • An ellipse
  • A parabola
  • A circle
  • A hyperbola
If the radius of the circle $$ x ^ { 2 } + y ^ { 2 } $$ - 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 $$\frac { (3x-4y-{ 1) }^{ 2 } }{ 100 } -\frac { (4x+3y-{ 1) }^{ 2 } }{ 225 } =1,$$ then
length latusrectum of hyperbola is-
  • $$\frac { 9 }{ 2 } $$
  • $$\frac { 40 }{ 3 } $$
  • 9
  • $$\frac { 8 }{ 3 } $$
If  $$y ^ { 2 } - 2 x - 2 y + 5 = 0$$  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 $$\alpha $$ for which three distinct chords drawn from $$(\alpha ,0)$$ to the ellipse $${ x }^{ 2 }+2{ y }^{ 2 }=1$$ are bisected by the parabola $${ y }^{ 2 }=4x$$ is 
  • $$9$$
  • $$\sqrt { 17 } $$
  • $$8$$
  • None of these.
The equation $$\dfrac{x^2}{10 - a} + \dfrac{y^2}{4 - a} = 1$$ , represents an ellipse , if 
  • $$a < 4$$
  • $$a > 4$$
  • $$4 < a < 10$$
  • $$a > 10$$
Let PQ be the latus rectum of the parabola $$y^2=4x$$ with vertex A. Minimum length of the projection of PQ on a tangent drawn in portion of parabola PAQ is :
  • $$2$$
  • $$4$$
  • $$2 \sqrt{3}$$
  • $$2 \sqrt{2}$$
$$C:\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{{12}} = 1$$ 
The equation of parabolas with same latus- rectum as conic C, is/are
  • $${y^2} - 5x + 3 = 0$$
  • $${y^2} +6x - 21 = 0$$
  • $${y^2} - 6x - 21 = 0$$
  • $${y^2} +6x + 3 = 0$$
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
  • $$

    3 x ^ { 2 } - y ^ { 2 } = 3

    $$
  • $$

    x ^ { 2 } - 3 y ^ { 2 } = 3

    $$
  • $$

    3 x ^ { 2 } - y ^ { 2 } = 9

    $$
  • $$

    x ^ { 2 } - 3 y ^ { 2 } = 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\left[ { \left( x-2 \right)  }^{ 2 }+{ \left( y-3 \right)  }^{ 2 } \right] ={ \left( 3x-4y+7 \right)  }^{ 2 }$$ is 
  • 4
  • 2
  • 1/5
  • 2/5
equation of latus rectum of the parabola $${ y }^{ 2 }-16x-6y+1=0$$ is
  • x-7=0
  • x+7=0
  • 2x-7=0
  • 2x+7=0
The latus rectum of a parabola whose directrix is x + y- 2 =0 and focus is (3, -4) is 
  • $$-3\sqrt { 2 } $$
  • $$3\sqrt { 2 } $$
  • $$2\sqrt { 2 } $$
  • $$3\sqrt { 2 } $$
The y-axis is the directrix of the ellipse with eccentricity e=1/2 and the corresponding focus is at (3, 0), equation to its auxilary circle is
  • $$x^2+y^2-8x+12=0$$
  • $$x^2+y^2-8x-12=0$$
  • $$x^2+y^2-8x+9=0$$
  • $$x^2+y^2=4$$
If e,e' be the eccentricities of two conics S and S' and if $$e^2+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 + y - 5 = 0$$ is
  • $${x^2} + {y^2} + 2x - 4y + 6 = 0$$
  • $${x^2} + {y^2} - 2x - 4y + 3 = 0$$
  • $${x^2} + {y^2} - 2x + 4y + 8 = 0$$
  • $${x^2} + {y^2} - 2x - 4y + 8 = 0$$
The equation of the ellipse with axes along the x-axis and the y-axis, which passes through the points P(4, 3) and Q (6, 2) is
  • $$\frac{x^2}{50}+\frac{y^2}{13}=1$$
  • $$\frac{x^2}{52}+\frac{y^2}{13}=1$$
  • $$\frac{x^2}{13}+\frac{y^2}{52}=1$$
  • $$\frac{x^2}{52}+\frac{y^2}{17}=1$$
If the circle describe on the line joining the points (0, 1) and $$(\alpha ,\beta )$$ as diameter cuts the x-axis in points whose abscissae are roots of equation $$x^2-x+3=0$$ the $$(\alpha ,\beta )$$
  • (1, 3)
  • (1, 5)
  • (-5, 1)
  • (-5, -1)
The equation of a circle with origin as a centre and passing through equilateral whose median is of length 3a is
  • $${ x }^{ 2 }+{ y }^{ 2 }={ 9a }^{ 2 }$$
  • $${ x }^{ 2 }+{ y }^{ 2 }={ 16a }^{ 2 }$$
  • $${ x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }$$
  • None of these
If the parabola $${ y }^{ 2 }=4ax$$ passes through (2,6) then the equation of the latusrectum is 
  • 2x -9 = 0
  • 4x + 9 = 0
  • 2x + 9 = 0
  • 4x - 9 = 0
The length of the latus rectum of the parabola  $$4 y ^ { 2 } + 2 x - 20 y + 17 = 0$$  is
  • $$3$$
  • $$6$$
  • $$1 / 2$$
  • None
The length of the latus rectum of the parabola $${ y }^{ 2 }-4x+4y+8=0\quad is$$
  • 8
  • 6
  • 4
  • 2
The equation  $$\dfrac { { x }^{ 2 } }{ 12-a } +\dfrac { { y }^{ 2 } }{ 4-a } =1$$ represent an ellipse, if:
  • $$a < 12$$
  • $$ a < 4$$
  • $$ a > 12$$
  • $$ a > 4$$
The equation of circles passing through (3,-6) touching both the axes is 
  • $$x^{2}+y^{2}-6x+6y+9=0$$
  • $$x^{2}+y^{2}+6x-6y+9=0$$
  • $$x^{2}+y^{2}-30x-30y+225=0$$
  • $$x^{2}+y^{2}-30x+30y+225=0$$
If $$a\neq b$$ the parametric equations $$x=a(cos \Theta +sin \Theta ),y=b(cos\Theta -sin\Theta )$$ represents
  • Hyperbola
  • A circle
  • An ellipse
  • A pair of straight lines
  • A parabola
A common tangent to the conics $${ x }^{ 2 }=6y$$ and $$2{ x }^{ 2 }-4{ y }^{ 2 }=9$$, is __________.
  • $$x+y=1$$
  • $$x-y=1$$
  • $$x+y=\dfrac { 9 }{ 2 }$$
  • $$x-y=\dfrac { 3 }{ 2 } $$
The latus rectum of a parabola whose focal chord is PSQ such that SP=3 and SQ=2 is given by 
  • 24/5
  • 12/5
  • 6/5
  • none of these
The eccentricity of  the hyperbola $$x^{2}-3y^{2}+1=0$$  is 
  • $$\frac{1}{2}$$
  • 1
  • 2
  • 3
If $$5x+9=0$$ is the directrix of the hyperbola $$16{x}^{2}-9{y}^{2}=144$$, then its correponding focus is:
  • $$\left( -\cfrac { 5 }{ 3 } ,0 \right) $$
  • $$(5,0)$$
  • $$(-5,0)$$
  • $$\left( \cfrac { 5 }{ 3 } ,0 \right) $$
If the centroid of an equilateral triangle is (1,1) and one of its vertices is (-1,2) then, equation of its circum circle is 
  • $$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}$$
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