CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 4 - MCQExams.com

If the straight line $$y=mx+c$$ is parallel to the axis of the parabola $$y^2=lx$$ and intersects the parabola at $$\left(\dfrac{c^2}{8}, c\right)$$ then the length of the latus rectum is 
  • $$2$$
  • $$3$$
  • $$4$$
  • $$8$$
The area of the circle represented by the equation $${(x+3)}^{2}+{(y+1)}^{2}=25$$ is
  • $$4\pi$$
  • $$5\pi$$
  • $$16\pi$$
  • $$25\pi$$
The radius of the circle passing through the point $$(6, 2)$$ and two of whose diameters are $$\displaystyle x+y=6$$ and $$\displaystyle x+2y=4$$ is:
  • $$4$$
  • $$6$$
  • $$20$$
  • $$\displaystyle \sqrt { 20 } $$
Write the equation of the circle with center at $$(0,0)$$ and a radius of $$6$$
  • $$(x-6)^2+y^2=36$$
  • $$x^2+(y-6)^2=0$$
  • $$x^2+y^2=36$$
  • $$x^2+y^2=-36$$
The graph of the equation $$x^2+2y^2

= 8$$ is
  • a circle
  • an ellipse
  • a hyperbola
  • a parabola
The graph of the equation $$4y^2 + x^2= 25$$ is
  • a circle
  • an ellipse
  • a hyperbola
  • a parabola
  • a straight line
Which of the following is an equation of the circle with its center at $$(0,0)$$ that passes through $$(3,4)$$ in the standard $$(x,y)$$ coordinate plane?
  • $$x+y=1$$
  • $$x-y=25$$
  • $${x}^{2}+y=25$$
  • $${x}^{2}+{y}^{2}=5$$
  • $${x}^{2}+{y}^{2}=25$$
What is the approximate radius of the circle whose equation is $$(x-\sqrt{3})^2+(y+2)^2=11$$?
  • 1.71
  • 2.33
  • 3.32
  • 3.85
  • 4.27
A circle with center $$(3, 8)$$ contains the point $$(2, -1)$$. Another point on the circle is:
  • $$(1, -10)$$
  • $$(4, 17)$$
  • $$(5, -9)$$
  • $$(7, 15)$$
  • $$(9, 6)$$
Identify the polynomial represented by the graph?
517085_9b27c0ab8bb7412bbe5f47959ac059e7.png
  • $$y = x^{2} + 2$$
  • $$y = -x^{2}$$
  • $$y = x^{2}$$
  • $$y = x^{2} - 2$$
Which of the following is an equation of a circle in the $$xy$$-plane with center $$\left(0, 4\right)$$ and a radius with endpoint $$\left(\dfrac{4}{3}, 5\right)$$?
  • $${ x }^{ 2 }+{ \left( y-4 \right) }^{ 2 }=\dfrac { 25 }{ 9 } $$
  • $${ x }^{ 2 }+{ \left( y+4 \right) }^{ 2 }=\dfrac { 25 }{ 9 } $$
  • $${ x }^{ 2 }+{ \left( y-4 \right) }^{ 2 }=\dfrac { 5 }{ 3 } $$
  • $${ x }^{ 2 }+{ \left( y+4 \right) }^{ 2 }=\dfrac { 3 }{ 5 } $$
The least value of $$2x^{2} + y^{2} + 2xy + 2x - 3y + 8$$ for real numbers $$x$$ and $$y$$ is
  • $$2$$
  • $$8$$
  • $$3$$
  • $$1$$
  • $$-\dfrac12$$
Locus of the point $$(\sqrt{3h} , \sqrt{3k + 2} )$$ if it lies on the line $$x-  y-  1 = 0$$ is a
  • Straight line
  • Circle
  • Parabola
  • None of these
The length of the latus rectum of the parabola whose vertex is $$(2, -3)$$ and the directrix $$x = 4$$ is
  • $$2$$
  • $$4$$
  • $$6$$
  • $$8$$
The graph of the equation $$x^2+\dfrac{y^2}{4}=1$$ is
  • an ellipse
  • a circle
  • a hyperbola
  • a parabola
  • two straight lines
Equation of circle with center (-a, -b) and radius $$\sqrt{a^2-b^2}$$ is.
  • $$x^2+y^2-2ax-2by - 2b^2=0$$
  • $$x^2+y^2-2ax-2by + 2a^2=0$$
  • $$x^2+y^2+2ax + 2by + 2b^2=0$$
  • $$x^2+y^2-2ax-2by + 2b^2=0$$
Which ordered number pair represents the center of the circle $$x^2 + y^2 - 6x + 4y - 12 = 0$$?
  • (9,4)
  • (3,2)
  • (3,-2)
  • (6,4)
The asymptotes of a hyperbola $$4x^2 - 9y^2=36$$ are
  • $$2x \pm 3y = 1$$
  • $$2x \pm 3y = 0$$
  • $$3x \pm 2y = 1$$
  • None
The equation of hyperbola whose coordinates of the foci are $$(\pm8,0)$$ and the lenght of latus rectum is $$24$$ units, is
  • $$3{ x }^{ 2 }-{ y }^{ 2 }=48$$
  • $$4{ x }^{ 2 }-{ y }^{ 2 }=48$$
  • $${ x }^{ 2 }-3{ y }^{ 2 }=48$$
  • $${ x }^{ 2 }-4{ y }^{ 2 }=48$$
The lines $$2x - 3y - 5 = 0$$ and $$3x -4y = 7$$ are diameters of a circle of area 154 sq units, then the equation of the circle is.( Use $$\pi = \dfrac{22}{7}$$)
  • $$x^2+y^2+2x-2y-62=0$$
  • $$x^2+y^2+2x-2y-47=0$$
  • $$x^2+y^2-2x+2y-47=0$$
  • $$x^2+y^2-2x-2y-62=0$$
The length of latus rectum of the ellipse $$4{ x }^{ 2 }+9{ y }^{ 2 }=36$$ is
  • $$\dfrac{4}{3}$$
  • $$\dfrac{8}{3}$$
  • $$6$$
  • $$12$$
Consider the parametric equation
$$x = \dfrac {a(1 - t^{2})}{1 + t^{2}}, y = \dfrac {2at}{1 + t^{2}}$$.
What does the equation represent?
  • It represents a circle of diameter $$a$$
  • It represents a circle of radius $$a$$
  • It represents a parabola
  • None of the above
What is the radius of the circle passing through the point $$(2, 4)$$ and having centre at the intersection of the lines $$x - y = 4$$ and $$2x + 3y + 7 = 0$$?
  • $$3$$ units
  • $$5$$ units
  • $$3 \sqrt 3$$ units
  • $$5 \sqrt 2$$ units
The differential equation $$(3x + 4y + 1)dx + (4x + 5y + 1) dy = 0$$ represents a family of
  • Circles
  • Parabolas
  • Ellipses
  • Hyperbolas
The line $$(x-2)\cos \theta +(y-2)\sin \theta =1$$ touches a circle for all value of $$\theta$$, then the equation of circle is
  • $$x^2+y^2-4x-4y+7=0$$
  • $$x^2+y^2+4x+4y+7=0$$
  • $$x^2+y^2-4x-4y-7=0$$
  • $$None\ of\ the\ above$$
The equation of the smallest circle passing through the points $$(2, 2)$$ and $$(3, 3)$$ is
  • $$x^{2} + y^{2} + 5x + 5y + 12 = 0$$
  • $$x^{2} + y^{2} - 5x - 5y + 12 = 0$$
  • $$x^{2} + y^{2} + 5x - 5y + 12 = 0$$
  • $$x^{2} + y^{2} - 5x + 5y + 12 = 0$$
Let $$ABCD$$ be a square of side length $$1$$. and $$\Gamma $$ a circle passing through $$B$$ and $$C$$, and touching $$AD$$. The radius of $$\Gamma $$ is
  • $$\cfrac { 3 }{ 8 } $$
  • $$\cfrac { 1 }{ 2 } $$
  • $$\cfrac { 1 }{ \sqrt { 2 } } $$
  • $$\cfrac { 5 }{ 8 } $$
If focii of $$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$$ coincide with the focii of $$\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$$ and eccentricity of the hyperbola is $$2$$, then
  • $$a^2+b^2=14$$
  • There is a director circle of the hyperbola
  • Centre of the director circle is $$(0,0)$$
  • Length of latus rectum of the hyperbola is $$12$$
If $$e_{1}$$ and $$e_{2}$$ are the eccentricities of two conics with $$e_{1}^{2} + e_{2}^{2} = 3$$, then the conics are.
  • Ellipses
  • Parabolas
  • Circles
  • Hyperbolas
The line segment joining the foci of the hyperbola $$x^{2} - y^{2} + 1 = 0$$ is one of the diameters of a circle. The equation of the circle is :
  • $$x^{2} + y^{2} = 4$$
  • $$x^{2} + y^{2} = \sqrt {2}$$
  • $$x^{2} + y^{2} = 2$$
  • $$x^{2} + y^{2} = 2\sqrt {2}$$
The ends of the latus rectum of the parabola $$x^{2} + 10x - 16y + 25 = 0$$ are
  • $$(3, 4), (-13, 4)$$
  • $$(5, -8), (-5, 8)$$
  • $$(3, -4), (13, 4)$$
  • $$(-3, 4), (13, -4)$$
The eccentricity of an ellipse $$9{ x }^{ 2 }+16{ y }^{ 2 }=144$$ is
  • $$\dfrac { \sqrt { 3 } }{ 5 } $$
  • $$\dfrac { \sqrt { 5 } }{ 3 } $$
  • $$\dfrac { \sqrt { 7 } }{ 4 } $$
  • $$\dfrac { 2 }{ 5 } $$
The directrix of a parabola is $$x+8=0$$ and its focus is at $$(4,3)$$. Then, the length of the latusrectum of the parabola is
  • $$5$$
  • $$9$$
  • $$10$$
  • $$12$$
  • $$24$$
The foci of the ellipse $$4{x}^{2}+9{y}^{2}=1$$ are
  • $$\left( \pm \cfrac { \sqrt { 3 } }{ 2 } ,0 \right) $$
  • $$\left( \pm \cfrac { \sqrt { 5 } }{ 2 } ,0 \right) $$
  • $$\left( \pm \cfrac { \sqrt { 5 } }{ 3 } ,0 \right) $$
  • $$\left( \pm \cfrac { \sqrt { 5 } }{ 6 } ,0 \right) $$
  • $$\left( \pm \cfrac { \sqrt { 5 } }{ 4 } ,0 \right) $$
If the eccentricity of the hyperbola $${ x }^{ 2 }-{ y }^{ 2 }\sec ^{ 2 }{ \alpha  } =5$$ is $$\sqrt { 3 } $$ times the eccentricity of the ellipse $${ x }^{ 2 }\sec ^{ 2 }{ \alpha  } +{ y }^{ 2 }=25$$, then the value of $$\alpha $$ is
  • $${ \pi }/{ 6 }$$
  • $${ \pi }/{ 4 }$$
  • $${ \pi }/{ 3 }$$
  • $${ \pi }/{ 2 }$$
For the parabola $${ y }^{ 2 }+8x-12y+20=0$$
  • Vertex is $$(2,6)$$
  • Focus is $$(0.6)$$
  • Latusrectum $$4$$
  • Axis $$y=6$$
The foci of the conic section
$$25{ x }^{ 2 }+16{ y }^{ 2 }-150x=175$$ are
  • $$\left( 0,\pm 3 \right) $$
  • $$\left( 0,\pm 2 \right) $$
  • $$\left( 3,\pm 3 \right) $$
  • $$\left( 0,\pm 1 \right) $$
The equation of directrix of the parabola $$y^{2} + 4y + 4x + 2 = 0$$ is
  • $$x = -1$$
  • $$x = 1$$
  • $$x = -\dfrac {3}{2}$$
  • $$x = \dfrac {3}{2}$$
The radius of the circle passing through the points $$(2,3),(2,7)$$ and $$(5,3)$$ is
  • $$5$$
  • $$4$$
  • $$\cfrac { 5 }{ 2 } $$
  • $$2$$
  • $$\sqrt { 5 } $$
The one end of the latusrectum of the parabola $${ y }^{ 2 }-4x-2y-3=0$$ is at
  • $$\left( 0,-1 \right) $$
  • $$\left( 0,1 \right) $$
  • $$\left( 0,-3 \right) $$
  • $$\left( 3,0 \right) $$
  • $$\left( 0,2 \right) $$
The lines $$y=x+\sqrt { 2 } $$ and $$y=x-2\sqrt { 2 } $$ are the tangent of certain circle. If the point $$\left( 0,\sqrt { 2 }  \right) $$ lies on this circle, then its equation is
  • $${ \left( x-\cfrac { 3 }{ 2\sqrt { 2 } } \right) }^{ 2 }+{ \left( y+\cfrac { 1 }{ 2\sqrt { 2 } } \right) }^{ 2 }=\cfrac { 9 }{ 4 } $$
  • $${ \left( x+\cfrac { 3 }{ 2\sqrt { 2 } } \right) }^{ 2 }+{ \left( y+\cfrac { 1 }{ 2\sqrt { 2 } } \right) }^{ 2 }=\cfrac { 9 }{ 4 } $$
  • $${ \left( x-\cfrac { 3 }{ 2\sqrt { 2 } } \right) }^{ 2 }+{ \left( y-\cfrac { 1 }{ 2\sqrt { 2 } } \right) }^{ 2 }=\cfrac { 9 }{ 4 } $$
  • None of the above
On the parabola $$y={ x }^{ 2 }$$, the point least distant from the straight line $$y=2x-4$$ is
  • $$\left( 1,1 \right) $$
  • $$\left( 1,0 \right) $$
  • $$\left( 1,-1 \right) $$
  • $$\left( 0,0 \right) $$
If the eccentricity of the ellipse $$a{ x }^{ 2 }+4{ y }^{ 2 }=4a,(a<4)$$ is $$\cfrac { 1 }{ \sqrt { 2 }  } $$, then its semi-minor axis is equal to
  • $$2$$
  • $$\sqrt { 2 } $$
  • $$1$$
  • $$\sqrt { 3 } $$
  • $$3$$
The lines $$2x-3y=5$$ and $$3x-4y=7$$ are the diameters of a circle of area $$154$$ sq.units. The equation of the circle is
  • $${ x }^{ 2 }+{ y }^{ 2 }+2x-2y=62$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+2y=47\quad $$
  • $${ x }^{ 2 }+{ y }^{ 2 }+2x-2y=47$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+2y=62\quad $$
The equation of the circle which touches the lines $$x = 0, y = 0$$ and $$4x + 3y = 12$$ is
  • $$x^{2} + y^{2} - 2x - 2y - 1 = 0$$
  • $$x^{2} + y^{2} - 2x - 2y + 3 = 0$$
  • $$x^{2} + y^{2} - 2x - 2y + 2 = 0$$
  • $$x^{2} + y^{2} - 2x - 2y + 1 = 0$$
  • $$x^{2} + y^{2} - 2x - 2y - 3 = 0$$
The eccentricity of the ellipse $$12x^2 + 7y^2 = 84 $$ is equal to :
  • $$ \dfrac {\sqrt5}{7} $$
  • $$ \sqrt{\dfrac {5}{7}} $$
  • $$ \dfrac {\sqrt5}{12} $$
  • $$ \dfrac {5}{7} $$
  • $$ \dfrac {7}{12} $$
Equations $$x = a\cos \theta$$ and $$y= b\sin \theta$$ represent a conic section whose eccentricity $$e$$ is given by
  • $$e^{2} = \dfrac {a^{2} + b^{2}}{a^{2}}$$
  • $$e^{2} = \dfrac {a^{2} + b^{2}}{b^{2}}$$
  • $$e^{2} = \dfrac {a^{2} - b^{2}}{a^{2}}$$
  • None of these
An ellipse has $$OB$$ as semi-minor axis, $$F$$ and $${ F }^{ ' }$$ its foci and the $$\angle FB{ F }^{ ' }$$ is a right angle. Then, the eccentricity of the ellipse is
  • $$\dfrac { 1 }{ \sqrt { 3 } } $$
  • $$\dfrac { 1 }{ 4 } $$
  • $$\dfrac { 1 }{ 2 } $$
  • $$\dfrac { 1 }{ \sqrt { 2 } } $$
The hyperbola $$\cfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\cfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$$ passes through the point $$\left( \sqrt { 6 } ,3 \right) $$ and the length of the latusrectum is $$\cfrac { 18 }{ 5 } $$. Then, the length of the transverse axis is equal to
  • $$5$$
  • $$4$$
  • $$3$$
  • $$2$$
  • $$1$$
The equation of the circumcircle of the triangle formed by the lines $$y + \sqrt{3} x = 6, y - \sqrt{3} x = 6$$ and $$y=0$$ is 
  • $$x^2+y^2+4x=0$$
  • $$x^2+y^2-4y=0$$
  • $$x^2+y^2-4y=12$$
  • $$x^2+y^2+4x=12$$
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