CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 3 - MCQExams.com

Find the  Lactus Rectum of  $$\displaystyle 9y^{2}-4x^{2}=36$$ 
  • $$ 9$$
  • $$6$$
  • $$11$$
  • $$15$$
The equation of a diameter of a circle is $$x+y=1$$ and the greatest distance of any point of the circle from the diameter is $$\dfrac{1}{\sqrt{2}}$$ .Then, a possible  equation of the circle can be
  • $$x^{2}+y^{2}-2x+4y=0$$
  • $$x^{2}+y^{2}-x-y=0$$
  • $$x^{2}+y^{2}+4x-2y=0$$
  • $$x^{2}+y^{2}+2x+4y=0$$
Two vertices of an equilateral triangle are $$(-1, 0)$$ and $$(1, 0)$$, and its third vertex lies above the $$x$$-axis. The equation of the circumcircle of the triangle is
  • $$x^{2}+y^{2}=1$$
  • $$\sqrt{3}\left ( x^{2}+y^{2} \right )+2y-\sqrt{3}=0$$
  • $$\sqrt{3}\left ( x^{2}+y^{2} \right )-2y-\sqrt{3}=0$$
  • none of these
The equation $$ \displaystyle 3x^{2}-2xy+y^{2}=0 $$ represents:
  • a circle
  • hyperbola
  • a pair of lines
  • none of these
Find the length of latus rectum of the parabola whose focus is the point $$\displaystyle \left ( 2,3 \right )$$ and directrix is the line  $$\displaystyle x-4y+3=0.$$ 
  • $$\dfrac{14}{\sqrt { 17 }} $$
  • $$\dfrac{17}{\sqrt { 17 }} $$
  • $$\dfrac{15}{\sqrt { 17 }} $$
  • $$\dfrac{10}{\sqrt { 17 }} $$
The length of the latus rectum of the parabola $$x=ay^2+by+c$$ is 
  • $$\displaystyle \frac{a}{4}$$
  • $$\displaystyle \frac{a}{3}$$
  • $$\displaystyle \frac{1}{a}$$
  • $$\displaystyle \frac{1}{4a}$$
On the line joining the points $$A (0,4)$$ and $$B (3, 0)$$, a square $$ABCD $$ is constructed on the side of the line away from the origin. Equation of the circle having centre at $$C$$ and touching the axis of $$x$$ is
  • $$x^{2} + y^{2} - 14x -6y + 49 = 0$$
  • $$x^{2} + y^{2}- 14x -6y + 9 = 0$$
  • $$x^{2} + y^{2}-6x -14y + 49 = 0$$
  • $$x^{2} + y^{2}-6x -14y + 9 = 0$$
If the lines $$2x+3y+1= 0$$ and $$3x-y-4= 0$$ lie along the diameter of a circle of circumference $$10\pi $$, then equation of circle be
  • $$x^{2}+y^{2}+2\left ( x+y \right )-23= 0$$
  • $$x^{2}+y^{2}-2\left ( x+y \right )-23= 0$$
  • $$x^{2}+y^{2}-2x+2y-23= 0$$
  • $$x^{2}+y^{2}+2x-2y-23= 0$$
The equation of circle with origin as center and passing through the vertices of an equilateral triangle whose median is of length $$3a$$ is
  • $${ x }^{ 2 }+{ y }^{ 2 }=9{ a }^{ 2 }$$
  • $${ x }^{ 2 }+{ y }^{ 2 }=16{ a }^{ 2 }$$
  • $${ x }^{ 2 }+{ y }^{ 2 }=4{ a }^{ 2 }$$
  • $${ x }^{ 2 }+{ y }^{ 2 }={ a }^{ 2 }$$
The lines $$2x -3y=5$$ and $$3x -4y =7$$ are the diameters of a circle of area $$154$$ square units. An equation of this circle is $$(\pi = 22/7)$$
  • $$ x^{2} + y^{2} + 2x -2y = 62$$
  • $$ x^{2} + y^{2} + 2x -2y = 47$$
  • $$ x^{2}+y^{2}-2x + 2y = 47$$
  • $$ x^{2} + y^{2} -2x + 2y = 62$$
The equation of circle with origin as a centre and passing through equilateral triangle whose median is of length $$3a$$ is
  • $$x^{2} + y^{2} = 9a^{2}$$
  • $$x^{2} + y^{2} = 16a^{2}$$
  • $$x^{2} + y^{2} = 4a^{2}$$
  • $$x^{2} + y^{2} = a^{2}$$
If two vertices of an equilateral triangle are $$(-1,0) $$ and $$(1, 0),$$ the equation of its circumcircle is
  • $$ \sqrt{3} x^{2} +\sqrt{3}y^{2} +2y -\sqrt{3} =0$$
  • $$2x^{2}+2y^{2}+\sqrt{3}y-2=0$$
  • $$ \sqrt{3} x^{2} +\sqrt{3}y^{2} -2y -\sqrt{3} =0$$
  • $$2x^{2}+2y^{2}-\sqrt{3}y-2=0$$
Find the latus rectum of the parabola $$x^2\, +\, 2y- 3x\, +\, 5\, =\, 0$$
  • $$1$$
  • $$2$$
  • $$4$$
  • $$8$$
The lines $$2x-3y=5$$ and $$3x-4y=7$$ are diameters of a circle of area $$154\ sq.\ units$$. The equation of the circle is-
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-2y=47$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-2y=62$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+2y=47$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+2y=62$$
Find the equation of the circle whose centre is the point of intersection of the lines $$2x-3y+4=0$$ and $$3x+4y-5=0$$ and passes through the origin.
  • $$17({ x }^{ 2 }+{ y }^{ 2 })+2x-44y=0$$
  • $$17({ x }^{ 2 }-{ y }^{ 2 })+2x+44y=0$$
  • $$17({ x }^{ 2 }+{ y }^{ 2 })-2x+44y=0$$
  • None of these
If two distinct chords of a parabola $$x^2\, =\, 4ay$$ passing through $$(2a, a)$$ are bisected on the line $$x + y = 1$$, then length of latus rectum can be
  • $$2$$
  • $$1$$
  • $$4$$
  • $$5$$
The equation of the  circle passing through $$(3,6)$$ and whose centre is $$(2,-1)$$ is-
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x+2y=45$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x-2y+45=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x-2y=45$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x+2y+45=0$$
The equation of the circle drawn with the focus of the parabola $$(x-1)^2 - 8y = 0$$ as its centre and touching the parabola at its vertex is
  • $$x^2+y^2 - 4y = 0$$
  • $$x^2+y^2 - 4y + 1=0$$
  • $$x^2+y^2 - 2x - 4y = 0$$
  • $$x^2 + y^2 - 2x - 4y + 1=0$$
The intercept on the line $$y=x$$ by the circle $${ x }^{ 2 }+{ y }^{ 2 }-2x=0$$ is $$AB$$. Equation of the circle with $$AB$$ as a diameter is
  • $${ x }^{ 2 }+{ y }^{ 2 }+x+y=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-x-y=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+x-y=0$$
  • None of these
The normal at the point $$(3, 4)$$ on a circle cuts the circle again at the point $$(1, 2)$$. Then the equation of the circle is -
  • $$\displaystyle { x }^{ 2 }+{ y }^{ 2 }-4x-6y+12=0$$
  • $$\displaystyle { x }^{ 2 }+{ y }^{ 2 }-4x+6y-12=0$$
  • $$\displaystyle { x }^{ 2 }+{ y }^{ 2 }-4x-6y+11=0$$
  • $$\displaystyle { x }^{ 2 }+{ y }^{ 2 }-4x+6y+11=0$$
The lines $$2x - 3y = 5 \ \ \& \ \ 3x - 4y = 7$$ are diameters of a circle of area 154 sq units. Then the equation of the circle is
  • $$\displaystyle x^{2}+y^{2}+2x-2y=62 $$
  • $$\displaystyle x^{2}+y^{2}-2x+2y=47 $$
  • $$\displaystyle x^{2}+y^{2}+2x-2y=47 $$
  • $$\displaystyle x^{2}+y^{2}-2x+2y=62 $$
For the points on the circle $$\displaystyle x^{2}+y^{2}-2x-2y+1=0$$, the sum of maximum and minimum values of $$4x + 3y$$ is 
  • $$\displaystyle \frac{26}{3}$$
  • $$10$$
  • $$12$$
  • $$14$$
The lines $$2x - 3y = 5$$ & $$3x - 4y = 7$$ are diameters of a circle of area $$154$$ sq units Then the equation of the circle is
  • $$\displaystyle x^{2}+y^{2}+2x-2y=62 $$
  • $$\displaystyle x^{2}+y^{2}-2x+2y=47 $$
  • $$\displaystyle x^{2}+y^{2}+2x-2y=47 $$
  • $$\displaystyle x^{2}+y^{2}-2x+2y=62 $$
The centre of a circle is $$( x -2 , x+1 )$$ and it passes through the points $$( 4 , 4 )$$ Find the value ( or values ) of $$x$$, if the diameter of the circle is of length $$\displaystyle 2\sqrt{5}$$ units. 
  • $$1$$ or $$3$$
  • $$-1$$ or $$4$$
  • $$5$$ or $$4$$
  • $$3$$ or $$-2$$
The equation circle whose center is $$(0,0)$$ and radius is $$4$$ is 
  • $$x^2+y^2=4$$
  • $$x^2+y^2=16$$
  • $$x^2+y^2=2$$
  • None.
The equation $$\displaystyle \frac {x^2}{8-t}\, +\, \displaystyle \frac {y^2}{t-4}\, =\, 1$$ will represent an ellipse if
  • $$t\, \in\, (1,\, 5)$$
  • $$t\, \in\, (2,\, 8)$$
  • $$t\, \in\, (4,\, 8)\, -\, \{6\}$$
  • $$t\, \in\, (4,\, 10)\, -\, \{6\}$$
Two circles touch each other externally at C and a common tangent touches them at A and B. Which one is true?
  • $$CD\perp AB$$
  • $$\angle ACB=90^o$$
  • $$AC=BC$$
  • All of these
Find the center-radius form of the equation of the circle with center $$\left( 4,0 \right) $$ and radius $$7$$
  • $${ \left( x-4 \right) }^{ 2 }+{ y }^{ 2 }=49$$
  • $${ x }^{ 2 }+{ \left( y+4 \right) }^{ 2 }=7$$
  • $${ x }^{ 2 }+{ \left( y-4 \right) }^{ 2 }=7$$
  • $${ \left( x+4 \right) }^{ 2 }+{ y }^{ 2 }=49$$
What is the equation of a circle with center (-3,1) and radius 7?
  • $$\displaystyle \left ( x-3 \right )^{2}+\left ( y+1 \right )^{2}=7$$
  • $$\displaystyle \left ( x-3 \right )^{2}+\left ( y+1 \right )^{2}=49$$
  • $$\displaystyle \left ( x+3 \right )^{2}+\left ( y-1 \right )^{2}=7$$
  • $$\displaystyle \left ( x+3 \right )^{2}+\left ( y-1 \right )^{2}=49$$
An ambulance company provides services within an 80 mile radius of their headquarters If this service area is represented graphically with the headquarters located at the coordinates (0, 0) what is the equation that represents the service area?
  • $$\displaystyle x^{2}+y^{2}=80$$
  • $$\displaystyle \left ( x-0 \right )^{2}+\left ( y-0 \right )^{2}=80$$
  • $$\displaystyle x^{2}+y^{2}=1600$$
  • $$\displaystyle x^{2}+y^{2}=6400$$
Graph the circle
$${ \left( x-3 \right)  }^{ 2 }+{ \left( y+4 \right)  }^{ 2 }=4$$
426427.png
The point $$P(9/2, 6)$$ lies on the parabola $$y^2=4ax$$, then parameter of the point P is
  • $$\frac{3a}{2}$$
  • $$\frac{2}{3a}$$
  • $$\frac{2}{3}$$
  • $$\frac{3}{2}$$
Find the equation of the circle with center on x + y = 4 and 5x + 2y + 1 = 0 and having a radius of 3
  • $$\displaystyle x^{2}+y^{2}+6x-16y+64=0$$
  • $$\displaystyle x^{2}+y^{2}+8x-14y+25=0$$
  • $$\displaystyle x^{2}+y^{2}+6x-14y+49=0$$
  • $$\displaystyle x^{2}+y^{2}+6x-14y+36=0$$
  • none of these
Find the equation of k for which the equation $$\displaystyle x^{2}+y^{2}+4x-2y-k=0$$ represents a point circle
  • $$5$$
  • $$-5$$
  • $$6$$
  • $$-6$$
  • none of these
The equation $$y^{2} + 4x + 4y + k = 0$$ represents a parabola whose latus rectum is
  • $$1$$
  • $$2$$
  • $$3$$
  • $$4$$
Equation of the parabola with its vertex at $$(1, 1)$$ and focus $$(3, 1)$$ is
  • $$(x 1)^2 = 8 (y - 1)$$
  • $$(y - 1)^2 = 8 (x - 3)$$
  • $$(y - 1)^2 = 8 (x - 1)$$
  • $$(x - 3)^2 = 8(y - 1)$$
The equation of a circle which has a tangent $$3x+4y=6$$ and two normals given by $$(x-1)(y-2)=0$$ is
  • $$(x-3)^2+(y-4)^2=5^2$$
  • $$x^2+y^2-4x-2y+4=0$$
  • $$x^2+y^2-2x-4y+4=0$$
  • $$x^2+y^2-2x-4y+5=0$$
The ends of the latus rectum of the conic $$x^{2} + 10x - 16y + 25 = 0$$ are
  • $$(3, -4), (13, 4)$$
  • $$(-3, -4), (13, -4)$$
  • $$(3, 4), (-13, 4)$$
  • $$(5, -8), (-5, 8)$$
The equation of the circle whose centre and radius are $$\left( 1,-1 \right) $$ and $$4$$ respectively, is
  • $${ x }^{ 2 }-{ y }^{ 2 }+2x+2y-14=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-2y-14=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x+2y-14=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-2x-2y+14=0$$
For hyperbola $$\dfrac{x^2}{cos^2a}-\dfrac{y^2}{sin^2a}=1$$ which of the following remains constant with change in 'a'?
  • Abscissae of vertices
  • Abscissae of foci
  • Eccentricity
  • Directrix
The equation of the ellipse having vertices at $$\displaystyle \left( \pm 5,0 \right) $$ and foci $$\displaystyle \left( \pm 4,0 \right) $$ is
  • $$\displaystyle \frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 } =1$$
  • $$\displaystyle 9{ x }^{ 2 }+25{ y }^{ 2 }=225$$
  • $$\displaystyle \frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 25 } =1$$
  • $$\displaystyle 4{ x }^{ 2 }+5{ y }^{ 2 }=20$$
The equation of a parabola which passes through the intersection of a straight line x$$+$$y$$=0$$ and the circle $$x^2+y^2+4y=0$$ is.
  • $$y^2=4x$$
  • $$y^2=x$$
  • $$y^2=2x$$
  • None of these
The distance between the foci of the hyperbola $${ x }^{ 2 }-3{ y }^{ 2 }-4x-6y-11=0$$ is
  • $$4$$
  • $$6$$
  • $$8$$
  • $$10$$
The equation to the circle with centre $$(2, 1)$$ and touching the line $$3x + 4y = 5$$ is
  • $$x^{2} + y^{2} - 4x - 2y + 5 = 0$$
  • $$x^{2} + y^{2} - 4x - 2y - 5 = 0$$
  • $$x^{2} + y^{2} - 4x - 2y + 4 = 0$$
  • $$x^{2} + y^{2} - 4x - 2y - 4 = 0$$
Find the equation of a circle with center $$(2,0)$$ and passing through point $$\left( 3,\sqrt { 3 }  \right) $$. 
  • $$(x - 2)^{2} + y^{2} = 4$$
  • $$(x + 2)^{2} + y^{2} = 4$$
  • $$(x - 2)^{2} + y^{2} = 16$$
  • $$(x + 2)^{2} + y^{2} = 16$$
If $$(a,b)$$ lies on circle with centre as origin, then its radius will be
  • $$\displaystyle a-b$$
  • $$\displaystyle a+b$$
  • $$\displaystyle \sqrt { { a }^{ 2 }+{ b }^{ 2 } } $$
  • $$\displaystyle { a }^{ 2 }+{ b }^{ 2 }$$
The radius of the circle $$x^{2} + y^{2} + 4x + 6y + 13 = 0$$ is
  • $$\sqrt {26}$$
  • $$\sqrt {13}$$
  • $$\sqrt {23}$$
  • $$0$$
The sum of the focal distances of any point on the conic $$\dfrac {x^{2}}{25} + \dfrac {y^{2}}{16} = 1$$ is
  • $$10$$
  • $$9$$
  • $$41$$
  • $$18$$
The point $$(3, 4)$$ is the focus and $$2x - 3y + 5 = 0$$ is the directrix of a parabola. Lenghth of  latus rectum is
  • $$\dfrac {2}{\sqrt {13}}$$
  • $$\dfrac {4}{\sqrt {13}}$$
  • $$\dfrac {1}{\sqrt {13}}$$
  • $$\dfrac {3}{\sqrt {13}}$$
If the centre $$O$$ of circle is the intersection of $$x-$$axis and line $$y=\dfrac { 4 }{ 3 } x+4$$, and the point $$(3,8)$$ lies on circle, then the equation of circle will be
  • $$\displaystyle { x }^{ 2 }+{ y }^{ 2 }=25$$
  • $$\displaystyle { \left( x+3 \right) }^{ 2 }+{ y }^{ 2 }=25$$
  • $$\displaystyle { \left( x+3 \right) }^{ 2 }+{ y }^{ 2 }=100$$
  • $$\displaystyle { \left( x+3 \right) }^{ 2 }+{ \left( y-8 \right) }^{ 2 }=100$$
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