CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 9 - MCQExams.com

Find the equation of a circle whose centre is (2, - 1 ) an radius is 3
  • $$

    x ^ { 2 } + y ^ { 2 } + 4 x - 2 y + 4 = 0

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } - 4 x + 2 y - 4 = 0

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } + 4 x + 2 y - 4 = 0

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } + 2 x - 4 y - 4 = 0

    $$
The equation of a circle which is passing through the vertices of an equilateral triangle whose median is of length 3 a is
  • $$

    x ^ { 2 } + y ^ { 2 } = 9 a ^ { 2 }

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } = 16 a ^ { 2 }

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } = 4 a ^ { 2 }

    $$
  • $$

    x ^ { 2 } + y ^ { 2 } = a ^ { 2 }

    $$
Equation $$\sqrt{(x-2)^2 + y^2} + \sqrt{(x+2)^2 + y^2}$$ = 4 represents _____________.
  • Parabola
  • Ellipse
  • Circle
  • straight lines
If $$\left| z-{ z }_{ 0 } \right| =\dfrac { \left| a\overline { z } +a\overline { z } +b \right|  }{ 2\left| a \right|  } $$ represent a parabola, Then the  length of latus  rectum of parabola 
  • $$\left| a\overline { { z }_{ 0 } } \overline { { a }z_{ 0 } } +b \right| $$
  • $$\dfrac { \left| a\overline { { z }_{ 0 } } \overline { { a }z_{ 0 } } +b \right| }{ \left| a \right| } $$
  • $$\dfrac { \left| a\overline { { z }_{ 0 } } \overline { { a }z_{ 0 } } +b \right| }{ 2\left| a \right| } $$
  • None of these
If the tangent to the curve, $$y=x^3+ax-b$$ at the point $$(1, -5)$$ is perpendicular to the line, $$-x+y+4=0$$, then which one of the following points lies on the curve?
  • $$(-2, 2)$$
  • $$(2, -2)$$
  • $$(2, -1)$$
  • $$(-2, 1)$$
In what ratio, the point of intersection of the common tangents to hyperbola $$\dfrac{x^2}{1}-\dfrac{y^2}{8}=1$$ and parabola $$y^2=12x$$, divides the foci of the given hyperbola?
  • $$3:4$$
  • $$3:2$$
  • $$5:4$$
  • $$5:3$$
$$AB$$ is a chord of the circle $$x^{2} + y^{2} = 9$$. The tangent at $$A$$ and $$B$$ intersect at $$C$$. If $$(1, 2)$$ is the midpoint of $$AB$$, the area of $$\triangle ABC$$ is (in square units).
  • $$9$$
  • $$\dfrac {7}{\sqrt {5}}$$
  • $$\dfrac {9}{\sqrt {5}}$$
  • $$\dfrac {8}{\sqrt {5}}$$
The equation $$\dfrac {x^{2}}{2 - \lambda} + \dfrac {y^{2}}{\lambda - 5} - 1 = 0$$ represents an ellipse, if
  • $$\lambda < 5$$
  • $$\lambda < 2$$
  • $$2 < \lambda < 5$$
  • $$\lambda < 2$$ or $$\lambda < 5$$
The eccentricity of the ellipse $$5x^{2} + 9y^{2} = 1$$ is
  • $$\dfrac 23$$
  • $$\dfrac 34$$
  • $$\dfrac 45$$
  • $$\dfrac 12$$
The eccentricity of the ellipse $$9x^{2} + 25y^{2} - 18x - 100y - 116 = 0$$, is
  • $$25/16$$
  • $$4/5$$
  • $$16/25$$
  • $$5/4$$
An ellipse has its centre at $$(1, -1)$$ and semi-major axis $$= 8$$ and it passes through the point $$(1, 3)$$. The equation of the ellipse is
  • $$\dfrac {(x + 1)^{2}}{64} + \dfrac {(y + 1)^{2}}{16} = 1$$
  • $$\dfrac {(x - 1)^{2}}{64} + \dfrac {(y + 1)^{2}}{16} = 1$$
  • $$\dfrac {(x - 1)^{2}}{16} + \dfrac {(y + 1)^{2}}{64} = 1$$
  • $$\dfrac {(x + 1)^{2}}{64} + \dfrac {(y - 1)^{2}}{16} = 1$$
The eccentricity of the ellipse $$25x^{2} + 16^{2} = 400$$ is
  • $$\dfrac 35$$
  • $$\dfrac 13$$
  • $$\dfrac 25$$
  • $$\dfrac 15$$
Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.
  • $$\cfrac{1}{\sqrt 3}$$
  • $$\cfrac{1}{\sqrt 5}$$
  • $$\cfrac{1}{\sqrt 2}$$
  • None of the above
If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to
  • $$\dfrac {1}{3}$$
  • $$\dfrac {1}{\sqrt {3}}$$
  • $$\dfrac {1}{\sqrt {2}}$$
  • $$\dfrac {2\sqrt {2}}{3}$$
  • $$\dfrac {2}{3\sqrt {2}}$$
If the latus-rectum of an ellipse is one half of its minor axis, then its eccentricity is
  • $$\dfrac {1}{2}$$
  • $$\dfrac {1}{\sqrt {2}}$$
  • $$\dfrac {\sqrt {3}}{2}$$
  • $$\dfrac {\sqrt {3}}{4}$$
The eccentricity of the conic $$9x^{2} + 25y^{2} = 225$$ is
  • $$\dfrac 25$$
  • $$\dfrac 45$$
  • $$\dfrac 13$$
  • $$\dfrac 15$$
  • $$\dfrac 35$$
The vertex of the parabola $$y^2 - 4y - x + 3 = 0$$ is
  • $$(-1,3)$$
  • $$(-1,2)$$
  • $$(2,-1)$$
  • $$(3, -1)$$
The eccentricity of the conic $$9{x}^{2}-16{y}^{2}=144$$ is
  • $$\cfrac{5}{4}$$
  • $$\cfrac{4}{3}$$
  • $$\cfrac{4}{5}$$
  • $$\sqrt{7}$$
 The equation $$5x^2 + y^2 + y = 8$$ represents 
  • An ellipse
  • A parabola
  • A hyperbola
  • A Circle
Write the length of the latus-rectum of the hyperbola $$16{x}^{2}-9{y}^{2}=144$$
  • $$\cfrac{5}{3}$$
  • $$\cfrac{4}{3}$$
  • $$\cfrac{3}{4}$$
  • $$\cfrac{4}{5}$$
The equation of the circle with centre $$(2, 2)$$ which passes through $$(4,5)$$ is 
  • $$x^2 + y^2 - 4x + 4y - 77 = 0$$
  • $$x^2 + y^2 - 4x - 4y - 5 = 0$$
  • $$x^2 + y^2 + 2x + 2y - 59 = 0$$
  • $$x^2 + y^2 - 2x - 2y - 23 = 0$$
  • $$x^2 + y^2 + 4x - 2y -26 = 0$$
The centre of the ellipse $$4x^2 + y^2 - 8x + 4y - 8 = 0$$ is
  • $$(0,2)$$
  • $$(2,-1)$$
  • $$(2,1)$$
  • $$(1,2)$$
The latus-rectum of the hyperbola $$16{x}^{4}-9{y}^{2}=144$$ is
  • $$16/3$$
  • $$32/3$$
  • $$8/3$$
  • $$4/3$$
The eccentricity of the ellipse $$\dfrac{(x-1)^2}{2} + \left(y + \dfrac{3}{4}\right)^2 = \dfrac{1}{16}$$ is
  • $$\dfrac{1}{\sqrt{2}}$$
  • $$\dfrac{1}{2\sqrt{2}}$$
  • $$\dfrac{1}{2}$$
  • $$\dfrac{1}{4}$$
The latus rectum of the parabola $$\displaystyle x = at^2 + bt + c, y = a't^2 + b't + c'$$ is
  • $$\displaystyle \dfrac {\left ( aa'- bb' \right )^2}{\left ( a^2 + a'^2 \right )^\dfrac {3}{2}}$$
  • $$\displaystyle \dfrac {\left ( ab'- a'b \right )^2}{\left ( a^2 + a'^2 \right )^\dfrac {3}{2}}$$
  • $$\displaystyle \dfrac {\left ( bb'- aa' \right )^2}{\left ( b^2 + b'^2 \right )^\dfrac {3}{2}}$$
  • $$\displaystyle \dfrac {\left ( a'b- ab' \right )^2}{\left ( b^2 + b'^2 \right )^\dfrac {3}{2}}$$
The foci of the ellipse $$25\left ( x + 1 \right )^2 + 9\left ( y + 2 \right )^2 = 225$$, are at
  • $$\left ( -1 , 2 \right )$$ and $$\left ( -1 , -6 \right )$$
  • $$\left ( -2 , 1 \right )$$ and $$\left ( -2 , 6 \right )$$
  • $$\left ( -1 , -2 \right )$$ and $$\left ( -2 , -1 \right )$$
  • $$\left ( -1 , -2 \right )$$ and $$\left ( -1 , -6 \right )$$
The centre of a circle is $$C(2,-5)$$ and the circle passes through the point $$A(3,2)$$. The equation of the circle is
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x+10y-21=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x+6y-21=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x-10y+21=0$$
  • none of these
If the parabola $${y}^{2}=4ax$$ passes through the point $$P(3,2)$$, then the length of its latus rectum is
  • $$\cfrac{1}{3}$$
  • $$\cfrac{2}{3}$$
  • $$\cfrac{4}{3}$$
  • $$4$$
The equation $$\displaystyle ax^2 + 4xy + y^2 + ax + 3y + 2 = 0$$ represents a parabola if a is
  • $$\displaystyle -4$$
  • $$\displaystyle 4$$
  • $$\displaystyle 0$$
  • $$\displaystyle 8$$
The latus rectum of the hyperbola $$9x^{2} - 16y^{2} - 18x - 32y - 151 = 0$$ is 
  • $$\dfrac{9}{4}$$
  • 9
  • $$\dfrac{3}{2}$$
  • $$\dfrac{9}{2}$$
If the eccentricity of the ellipse $$\dfrac{x^{2}}{a^{2}+ 1}+ \dfrac{y^{2}}{a^{2}+ 2}=1 \, is \, \dfrac{1}{\sqrt{6}}$$ , then latus rectrum of ellipse is 
  • $$\dfrac{5}{\sqrt{6}}$$
  • $$\dfrac{10}{\sqrt{6}}$$
  • $$\dfrac{8}{\sqrt{6}}$$
  • none of these
The co- ordinates (2,3) and (1,5)are the foci of an ellipse which passes through the origin , then the equation of 
  • tangent at the origin is $$(3 \sqrt{2}-5)x+ (1-2 \sqrt{2})y=0$$
  • tangent at the origin is $$(3 \sqrt{2}+ 5)x+ (1+2 \sqrt{2}y)=0$$
  • normal at the origin is ($$3\sqrt{2}+ 5)x -(2 \sqrt{2}+1 )y=0$$
  • normal at the origin is x$$(3 \sqrt{2}-5) -y(1- 2 \sqrt{2})=0$$
If the equation of the ellipse is $$3x^{2}+ 2 y^{2}+6x-8y+5=0, $$ then which of the following is/ are true?
  • $$e=\dfrac{1}{\sqrt{3}}$$
  • center is (-1,2)
  • foci are (-1,1) and (-1,3)
  • directrices are $$y= 2 \pm \sqrt{3}$$
Consider the parabola whose focus is at (0,0) and tangent at vertex is $$ x-y+1=0 $$

The length of latus rectum is
  • $$ 4 \sqrt{2} $$
  • $$ 2 \sqrt{2} $$
  • $$ 8 \sqrt{2} $$
  • $$ 3 \sqrt{2} $$
The length of the latus rectum of the parabola whose focus is $$\left (\frac{u^{2}} {2g} \sin 2\alpha, -\frac{u^{2}} {2g} \cos 2 \alpha  \right )$$ and directrix is $$y = \frac{u^{2}} {2g}$$ is 
  • $$\frac{u^{2}} {2g} \cos^{2} \alpha$$
  • $$\frac{u^{2}} {2g} \cos 2 \alpha$$
  • $$\frac{2u^{2}} {2g} \cos 2 \alpha$$
  • $$\frac{2u^{2}} {2g} \cos^{2} \alpha$$
The centre of a circle whose end points of a diameter are $$(-6,3)$$ and $$(6,4)$$ is
  • $$(8,-1)$$
  • $$(4,7)$$
  • $$(0,\frac{7}{2})$$
  • $$(4,\frac{7}{2})$$
The graph of $$y=x^2$$ is a straight line.
  • True
  • False
$$ \text{If (0, 0) be the vertex and } 3x- 4y+ 2 = 0 \text{ be the directrix of a parabola,}$$
$$\text{ then the length of its latus rectum is - } $$
  • $$\dfrac{4}{5}$$
  • $$\dfrac{2}{5}$$
  • $$\dfrac{8}{5}$$
  • $$\dfrac{1}{5}$$
The distance between the foci of an ellipse is 16 and eccentricity is $$\dfrac12$$. Length of the major axis of the ellipse is
  • 8
  • 64
  • 16
  • 32
$$\text{The length of the latus rectum of the parabola } x= ay^2+by+c \text{ is -}$$
  • $$\dfrac{a}{4}$$
  • $$\dfrac{a}{3}$$
  • $$\dfrac{1}{a}$$
  • $$\dfrac{1}{4a}$$
The hyperbola $$\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$$ has its conjugate axis of length $$5$$ and passes through the point $$(2, 1)$$. The length of latus rectum is :
  • $$\dfrac{5}{4}\sqrt{29}$$
  • $$\dfrac{5}{8}\sqrt{29}$$
  • $$\sqrt{29}$$
  • $$\dfrac{\sqrt{29}}{4}$$
The graph of the curve $$x^2 + y^2 - 2xy - 8x - 8y + 32 = 0$$ falls wholly in the
  • first quadrant
  • second quadrant
  • third quadrant
  • none of these
$$f(\displaystyle \mathrm{m}_{\mathrm{i}}, \frac{1}{\mathrm{m}_{\mathrm{i}}})$$ , $$\mathrm{i}=1,2,3,4$$ are four distinct points on the circle with centre origin, then value of $$\mathrm{m}_{1}\mathrm{m}_{2}\mathrm{m}_{3}\mathrm{m}_{4}$$ is equal to
  • $$0$$
  • $$-1$$
  • $$1$$
  • $$-a^{2}$$
lf the equation $$136 (x^{2}+y^{2})=(5x+3y+7)^{2}$$ represents a conic, then its length of latus rectum is
  • $$\displaystyle \frac{7}{2\sqrt{34}}$$
  • $$\displaystyle \frac{7}{\sqrt{34}}$$
  • $$\displaystyle \frac{14}{\sqrt{34}}$$
  • $$\displaystyle \frac{9}{\sqrt{34}}$$
A point $$P(x, y)$$ moves in $$XY$$ plane such that $$x = a\cos^2 \theta$$ and $$y = 2a \sin \theta$$, where $$\theta$$ is a parameter. The locus of the point $$P$$ is
  • circle
  • ellipse
  • unbounded parabola
  • part of a parabola
Let P point on the circle $$x^2 + y^2 = 9$$, Q a point on the line $$7x + y + 3 = 0$$, and the perpendicular bisector of PQ be the line $$x - y + 1 = 0$$. Then the coordinate of P are
  • (0, -3)
  • (0, 3)
  • $$\displaystyle \left ( \frac{72}{25}, -\frac{21}{25} \right)$$
  • $$\displaystyle \left ( -\frac{72}{25}, \frac{21}{25} \right)$$
The length of latus rectum of the parabola whose parametric equations are $$ x = t^{2} + t + 1$$, $$y = t^{2}-  t + 1$$, where $$t \in R$$, is equal to?
  • $$\sqrt{2}$$
  • $$\sqrt{4}$$
  • $$\sqrt{8}$$
  • $$\sqrt{6}$$
For the variable, the locus of the point of intersection of the lines $$3tx-2y+6t=0$$ and $$3x+2ty-6=0$$ is
  • the ellipse $$\cfrac { { x }^{ 2 } }{ 4 } +\cfrac { { y }^{ 2 } }{ 9 } =1$$
  • the ellipse $$\cfrac { { x }^{ 2 } }{ 9 } +\cfrac { { y }^{ 2 } }{ 4 } =1$$
  • the hyperbola $$\cfrac { { x }^{ 2 } }{ 4 } -\cfrac { { y }^{ 2 } }{ 9 } =1$$
  • the hyperbola $$\cfrac { { x }^{ 2 } }{ 9 } -\cfrac { { y }^{ 2 } }{ 4 } =1$$
If the line $$3x+4y=24$$ and $$4x+3y=24$$ intersects the coordinates axes at $$A,B,C$$ and $$D$$, then the equation of the circle passing through these $$4$$ points  is
  • $$x^{2}+y^{2}-12x-12y+48=0$$
  • $$x^{2}+y^{2}-14x-14y+48=0$$
  • $$x^{2}+y^{2}-12x-12y+46=0$$
  • $$x^{2}+y^{2}-14x-14y+46=0$$
The equation of a straight line drawn through the focus of the parabola $$y^2=-4x$$ at an angle of $$120^o$$ to the $$x$$-axis is.
  • $$y+\sqrt 3(x-1)=0$$
  • $$y-\sqrt 3(x-1)=0$$
  • $$y+\sqrt 3(x+1)=0$$
  • $$y-\sqrt 3(x+1)=0$$
0:0:1


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