CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 1 - MCQExams.com

If the lines $$2\mathrm{x}+3\mathrm{y}+1=0$$ and $$\mathrm{3x}- \mathrm{y}-4=0$$ lie along diameters of a circle of circumference $$ 10\pi$$, then the equation of the circle is: 
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}-2\mathrm{x}+2\mathrm{y}-23=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}-2\mathrm{x}-2\mathrm{y}-23=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+2\mathrm{x}+2\mathrm{y}-23=0$$
  • $$\mathrm{x}^{2}+\mathrm{y}^{2}+2\mathrm{x}-2\mathrm{y}-23=0$$
The circle $$x^{2}+y^{2}-8x=0$$ and hyperbola $$\dfrac{x^{2}}{9}-\dfrac{y^{2}}{4}=1$$ intersect at the points $$A$$ and $$B$$.
then the equation of the circle with $$AB$$ as its diameter is
  • $$x^{2}+y^{2}-12x+24=0$$
  • $$x^{2}+y^{2}+12x+24=0$$
  • $$x^{2}+y^{2}+24x-12=0$$
  • $$x^{2}+y^{2}-24x-12=0$$
The length of the latus rectum of the parabola $$169 \left[(x-1)^2+(y-3)^2\right]=(5x-12y+17)^2$$ is:
  • $$\displaystyle \frac { 14 }{ 13 } $$
  • $$\displaystyle \frac { 12 }{ 13 } $$
  • $$\displaystyle \frac { 28 }{ 13 } $$
  • $$none\ of\ these$$
Equation of the ellipse in its standard form is $$\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$
  • True
  • False
  • Nither
  • Either
The equation of the circle touching $$x = 0, y = 0$$ and $$x = 4$$ is
  • $$x^2 + y^2 - 4x - 4y + 16 = 0$$
  • $$x^2 + y^2 - 8x - 8y + 16 = 0$$
  • $$x^2 + y^2 + 4x + 4y + 4 = 0$$
  • $$x^2 + y^2 - 4x - 4y + 4 = 0$$
The radius of the circle with center (0,0) and which passes through (-6,8) is
  • 5
  • 10
  • 6
  • 8
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Assertion is incorrect but Reason is correct
The equation of circle with its centre at the origin is $$x^2+y^2=r^2$$
  • True
  • False
  • Neither
  • Either
Which of the following equations of a circle has center at (1, -3) and radius of 5?
  • $$\displaystyle x^{2}+y^{2}=25$$
  • $$\displaystyle \left ( x-1 \right )^{2}+\left ( y+3 \right )^{2}=25$$
  • $$\displaystyle \left ( x-1 \right )^{2}+\left ( y-3 \right )^{2}=25$$
  • $$\displaystyle \left ( x+1 \right )^{2}+\left ( y-3 \right )^{2}=25$$
Determine the area enclosed by the curve $$\displaystyle x^{2}-10x+4y+y^{2}=196$$
  • $$15\pi$$
  • $$225\pi$$
  • $$20\pi$$
  • $$17\pi$$
The standard equation of circle at origin is
  • $$x^2+y^2=r^2$$
  • $$x^2-y^2=r$$
  • $$x^2+y^2=1$$
  • $$x^2+y^2=0$$
The diameter of a circle described by $$\displaystyle 9x^{2}+9y^{2}=16$$ is
  • $$\dfrac {16}9$$
  • $$\dfrac 43$$
  • $$4$$
  • $$\dfrac 83$$
A circle has a diameter whose ends are at (-3, 2) and (12, -6) Its Equation is
  • $$\displaystyle 4x^{2}+4y^{2}-36x+16y+192=0$$
  • $$\displaystyle 4x^{2}+4y^{2}-36x+16y-192=0$$
  • $$\displaystyle 4x^{2}+4y^{2}-36x-16y-192=0$$
  • $$\displaystyle 4x^{2}+4y^{2}-36x-16y+192=0$$
What is the nature of the given graph?
517088_8a9b5c2904db443b8b64b96ae08c8fcd.png
  • The graph in symmetric about x-axis
  • The graph in symmetric about y-axis
  • Sum of x-intercept and y-intercept is greater than zero
  • The polynomial has $$3$$ terms
Find the equation of a circle with center $$(0, 0)$$ and radius $$5$$.
  • $$x^2+y^2=5$$
  • $$x^2-y^2=25$$
  • $$x^2+y^2=25$$
  • $$(x-1)^2+(y+1)^2=25$$
What is the radius of the circle with the following equation?
$$\displaystyle x^{2}-6x+y^{2}-4y-12=0$$
  • $$3.46$$
  • $$5$$
  • $$7$$
  • $$6$$
The locus of a planet orbiting around the sun is: 
  • A circle
  • A straight line
  • A semicircle
  • An ellipse
Number of intersecting points of the conic $$4x^{2} + 9y^{2} = 1$$ and $$4x^{2} + y^{2} = 4$$ is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$0$$ (zero)
The point (3,4) is the focus and $$2x-3y+5=0$$ is the directrix of a parabola .Its latus rectum is 
  • $$\dfrac{2}{\sqrt{13}}$$
  • $$\dfrac{4}{\sqrt{13}}$$
  • $$\dfrac{1}{\sqrt{13}}$$
  • $$\dfrac{3}{\sqrt{13}}$$
The circle with radius $$1$$ and centre being foot of the perpendicular from $$(5, 4)$$ on y-axis, is?
  • $$x^2+y^2-8x-15=0$$
  • $$x^2+y^2-10x+24=0$$
  • $$x^2+y^2-8y+15=0$$
  • $$x^2+y^2+2y=0$$
Equation of the circle with centre on y-axis and passing through the points $$(1,0),(1,1)$$ is:
  • $${ x }^{ 2 }+{ y }^{ 2 }-y-1=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-x-1=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-x+1=0\quad $$
  • $${ x }^{ 2 }+{ y }^{ 2 }-y+1=0$$
State whether the following statements are true or false.
The equation $$x^{2}+y^{2} + 2x -10y + 30 = 0$$ represents the equation of a circle.
  • True
  • False
The equation of the ellipse whose equation of directrix is $$3x+4y-5=0$$, coordinates of the focus are $$(1,2)$$ and the eccentricity is $$\dfrac{1}{2}$$ is $$91x^2+84y^2-24xy-170x-360y+475=0$$
  • True
  • False
Centres of the three circles
$${x}^{2}+{y}^{2}-4x-6y-14=0$$ 
$${x}^{2}+{y}^{2}+2x+4y-5=0$$ and
$${x}^{2}+{y}^{2}-10x-16y+7=0$$. The centres of the circles are:
  • are the vertices of a right angle
  • the vertices of an isosceles triangle which is not regular
  • vertices of a regular triangle
  • are collinear
The radius of the circle centred at $$(4,5)$$ and passing through the centre of the circle $${x}^{2}+{y}^{2}+4x+6y-12=0$$ is
  • $$2\sqrt {5}$$
  • $$2\sqrt {10}$$
  • $$3\sqrt {5}$$
  • $$3\sqrt {10}$$
Centre of circle whose normal's are $$x^{2}-2xy-3x+6y=0$$, is 
  • $$\left(3,\ \dfrac{3}{2}\right)$$
  • $$\left(3,\ -\dfrac{3}{2}\right)$$
  • $$\left(\dfrac{3}{2},\ 3\right)$$
  • $$None\ of\ these$$
The centre of the circle $$x^2+y^2+10x-20y+100=0$$ is 
  • $$(5,10)$$
  • $$(-5,10)$$
  • $$(-5,-10)$$
  • $$(5,-10)$$
The length of the diameter of the circle $${x^2} + {y^2} - 4x - 6y + 4 = 0$$
  • $$9$$
  • $$3$$
  • $$4$$
  • $$6$$
which of the following equations represents a parabola 
  • $${\left( {x - y} \right)^3} = 3$$
  • $$\frac{x}{y} - \frac{y}{x} = 0$$
  • $$\frac{x}{y} + \frac{4}{x} = 0$$
  • $${\left( {x + y} \right)^2} + 3 = 0$$
The locus of a point which is at a constant distance 5 from the fixed point $$(2,3)$$ is:
  • $${x^2} + {y^2} - 4x - 6y - 12 = 0$$
  • $${x^2} + {y^2} + 4x - 6y - 12 = 0$$
  • $${x^2} + {y^2} + 4x + 6y + 12 = 0$$
  • $${x^2} + {y^2} - 4x - 6y + 12 = 0$$
The equation of the circle passing through $$(3, 6)$$ and whose centre is $$(2, -1)$$ is 
  • $${x^2} + {y^2} - 4x + 2y = 45$$
  • $${x^2} + {y^2} - 2y + 45 = 0$$
  • $${x^2} + {y^2} + 4x - 2y = 45$$
  • $${x^2} + {y^2} + 2y + 45 = 0$$
Find the equation of the circle : 
Centered at $$(3,-2)$$ with radius $$4$$. 
  • $$x^2+y^2+6x-4y=3$$
  • $$x^2+y^2-6x+4y=3$$
  • $$x^2+y^2-3x+2y=-3$$
  • $$x^2+y^2+3x-2y=-3$$
The equation to the circle with centre $$(2,1)$$ and touches the line $$3x+4y-5$$ is ?
  • $$x^{2}+y^{2}-4x-2y+5=0$$
  • $$x^{2}+y^{2}-4x-2y-5=0$$
  • $$x^{2}+y^{2}-4x-2y+4=0$$
  • $$x^{2}+y^{2}-4x-2y-4=0$$
If the vertices of a triangle are $$(2, -2), (-1, -1)$$ and $$(5, 2)$$ then the equation of its circumcircle is?
  • $$x^2+y^2+3x+3y+8=0$$
  • $$x^2+y^2-3x-3y-8=0$$
  • $$x^2+y^2-3x+3y+8=0$$
  • None of these
Length of the latus rectum of the hyperbola $$xy=c^{2}$$, is
  • $$2c$$
  • $$\sqrt{2}c$$
  • $$2\sqrt{2}c$$
  • $$4c$$
For what value of $$k$$, does the equation $$9{x^2} + {y^2} = k\left( {{x^2} - {y^2} - 2x} \right)$$ represents equation of a circle?
  • $$1$$
  • $$2$$
  • $$-1$$
  • $$4$$
The length of latus recturn of the hyperbola
$${ 9x }^{ 2 }-16{ y }^{ 2\quad }+72x-32y-16=0$$
  • $$\dfrac { 9 }{ 2 }$$
  • $$\dfrac {- 9 }{ 2 } $$
  • $$\dfrac { 32 }{ 3 } $$
  • $$\dfrac { -32 }{ 2 } $$
Equation of the hyperbola with eccentricity $$\cfrac{3}{2}$$ and foci at $$(\pm 2, 0)$$ is
  • $$\cfrac{x^2}{4}-\cfrac{y^2}{5}=\cfrac{4}{9}$$
  • $$\cfrac{x^2}{9}-\cfrac{y^2}{4}=\cfrac{4}{9}$$
  • $$\cfrac{x^2}{4}-\cfrac{y^2}{9}=1$$
  • none of these
The centre of the circle given by $$\mathbf { r } \cdot ( \mathbf { i } + 2 \mathbf { j } + 2 \mathbf { k } ) = 15 \text { and } | \mathbf { r } - ( \mathbf { j } + 2 \mathbf { k } ) | = 4 ,$$
  • $$( 0,1,2 )$$
  • $$( 1,3,4 )$$
  • $$( - 1,3,4 )$$
  • None of these
The equation of the circle passing through (2,0) and (0,4) and having the minimum radius is 
  • $${ x }^{ 2 }+{ y }^{ 2 }=20$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-4y=0$$
  • $${ (x }^{ 2 }+{ y }^{ 2 }-4)+\lambda ({ x }^{ 2 }+{ y }^{ 2 }-16)=0$$
  • N.O.T.
Which is not represented by quadratic equation ?
  • Circle
  • Straight line
  • Parabola
  • Hyperbola
Find the area of $$x^2+y^2=49$$
  • 154
  • 49
  • 88
  • None
The equation $${ x }^{ 2 }+{ y }^{ 2 }=9$$ meets x-axis at 
  • $$(\pm 3,0)$$
  • $$(\pm 9,0)$$
  • $$(\pm 1,0)$$
  • (-5/14, 5/14)
If the  the hyperbola $$\frac { { x }^{ 2 } }{ 4 } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1$$ passses though $$(4,3)$$
  • $${ b }^{ 2 }=3 $$
  • $${ b }^{ 2 }=9$$
  • $${ b }^{ 2 }=4$$
  • $${ b }^{ 2 }=100$$
The equation $$\dfrac {x^{2}}{2-r}+\dfrac {y^{2}}{r-5}+1=0$$ represents an ellipse, if
  • $$r > 2$$
  • $$2 < r < 5$$
  • $$r > 5$$
  • $$r \in (2,5)$$
Find the value of a if $$y^2=4ax $$ pases through $$(8,8)$$
  • 2
  • 4
  • 8
  • None
Find the Center of circle $$x^2+y^2-4x-8x+25=0$$
  • $$(2,4)$$
  • $$(-2,-4)$$
  • $$(4,2)$$
  • $$(-4,-2)$$
The equation of the circle passing through $$(2,0)$$ and $$(0,4)$$ and having the minimum radius is ______________.
  • $${ x }^{ 2 }+{ y }^{ 2 }=4$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+4y=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-x-2y=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-4y=0$$
Radius of the circle $$2x^2+2y^2+8x+4y-3=0$$ is
  • $$\sqrt{17}$$
  • $$\sqrt{23}$$
  • $$\sqrt{\dfrac{13}{2}}$$
  • $$\sqrt{\dfrac{11}{2}}$$
A rod $${A}{B}$$ of length $$4$$ units moves horizontally with its left end $$\mathrm{A}$$ always on the circle $$x^{2}+y^{2}-4x-18y-29=0$$ then the locus of the other end $$\mathrm{B}$$ is
  • $$x^{2}+y^{2}-12x-8y+3=0$$
  • $$x^{2}+y^{2}-12x-18y+3=0$$
  • $$x^{2}+y^{2}+4x-18y-29=0$$
  • $$x^{2}+y^{2}-4x-16y+19=0$$
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