CBSE Questions for Class 11 Engineering Maths Conic Sections Quiz 8 - MCQExams.com

The intercept on the line $$y = x$$ by the circle $${x^2} + {y^2} - 2x = 0$$ is $$AB$$. The equation of the circle with $$AB$$ as a diameter, is
  • $${x^2} + {y^2} + x + y = 0$$
  • $${x^2} + {y^2} = x + y$$
  • $${x^2} + {y^2} - 3x + y = 0$$
  • None of the above
The equation of the circle passing through the points of intersection of the lines $$2x+y=0,\ x+y+3=0$$ and $$x-2y=0$$ is
  • $$x^{2}+y^{2}-x+7y=0$$
  • $$x^{2}+y^{2}+x-7y=0$$
  • $$x^{2}+y^{2}-x-7y=0$$
  • $$x^{2}+y^{2}+x+7y=0$$
Length of the latus rectum of the parabola $$25 [(x- 2)^{2}+(y-3)^{2}]=(3x-4y+7)^2 $$ is :
  • 4
  • 2
  • 1/5
  • 2/5
The equation of the circle which touches both the axes and the line $$\frac { x }{ 3 } +\frac { y }{ 4 } =1$$ and lies in the first quadrant is $$(x-c)^{ 2 }+(y-c)^{ 2 }={ c }^{ 2 }$$ where c is 
  • 1
  • 2
  • 4
  • 6
The length of the latus rectum of the parabola $$x^{2}-4x-8y+12=0$$ is-
  • $$4$$
  • $$6$$
  • $$8$$
  • $$10$$
The equation of the circle of a radius $$5$$ in the first quadrant which touches the x-axis and the line $$3x-4y=0$$ is 
  • $$x^{2}+y^{2}-24x-y-25=0$$
  • $$x^{2}+y^{2}-20x-12y+144=0$$
  • $$x^{2}+y^{2}-16x-18y+64=0$$
  • $$x^{2}+y^{2}-30x-10y+255=0$$
Equation of circle touching $$x=0, y=0$$ and $$x=4$$ is 
  • $$4(x^{2}+y^{2})-16x-16y+16=0$$
  • $$4(x^{2}+y^{2})-12x-12y+12=0$$
  • $$4(x^{2}+y^{2})-8x-8y+4=0$$
  • $$x^{2}+y^{2}-x-y-1=0$$
The area of the triangle formed by the tangent and the normal to the parabola $${ y }^{ 2 }=4ax,$$ both drawn at the same end of the latus rectum and the axis of the parabola is
  • $$2\sqrt { 2 } { a }^{ 2 }$$
  • $$2{ a }^{ 2 }$$
  • $$4{ a }^{ 2 }$$
  • None of these
Find the equation of a circle whose center is (2,-1) and radius is 3 
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x-2y+4=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x+2y-4=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+4x+2y-4=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+2x-4y-4=0$$
The vertex and focus of a parabola are $$(-2,2),(-6,6)$$. Then its length of latus rectum is
  • $$8\sqrt {2}$$
  • $$4\sqrt {2}$$
  • $$16\sqrt {2}$$
  • $$12\sqrt {2}$$
The equation of the tangent to the curve y = 2sinx + sin2x at $$x=\frac { \pi  }{ 3 } $$ on it is 
  • $$(2,3)$$
  • $$y+\sqrt { 3 } =0$$
  • $$2t-3=0$$
  • $$2y-3\sqrt { 3 } =0$$
The order of the differential equation of the family of parabolas whose length of latus rectum is fixed and axis is the X-axis 
  • $$2$$
  • $$1$$
  • $$3$$
  • $$4$$
$${ \cos }^{ 4 }\dfrac { \pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 3\pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 5\pi  }{ 8 } +{ \cos }^{ 4 }\dfrac { 7\pi  }{ 8 } =$$
  • $$\cfrac { 1 }{ 2 } $$
  • $$\cfrac { 3 }{ 2 } $$
  • $$\cfrac { 1 }{ 4 } $$
  • $$\cfrac { 3 }{ 4 } $$
Length of the latusrectum of the hyperbola $$xy-3x-4y+8=0$$ is 
  • $$4$$
  • $$4\sqrt{2}$$
  • $$8$$
  • $$None\,of\,these$$
The latus rectum of the hyperbola $$16{x^2} - 9{y^2} = 144$$ is-
  • $$\dfrac{13}{6}$$
  • $$\dfrac{32}{3}$$
  • $$\dfrac{8}{3}$$
  • $$\dfrac{4}{3}$$
The equation $$14x^{2}-4xy+11y^{2}-44x-58y+71=0$$ represents
  • a circle
  • an ellipse
  • a hyperbola
  • a rectangular hyperbola
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:
  • $$4$$
  • $$2$$
  • $$\dfrac {1}{5}$$
  • $$\dfrac {2}{5}$$
Length of the latus rectum of the hyperbola $$xy-3x-4y+8=0$$
  • $$4$$
  • $$4\sqrt{2}$$
  • $$8$$
  • none of these
The line $$y=mx+c$$ cut the circle $${x}^{2}+{y}^{2}={a}^{2}$$ in the distinct point $$A$$ and $$B$$. Equation of the circle having minimum radius that an be drawn through the points $$A$$ and $$B$$ is
  • $$\left( 1+{ m }^{ 2 } \right) \left( { x }^{ 2 }+{ y }^{ 2 }-{ a }^{ 2 } \right) +2c\left( y-mx-c \right) =0$$
  • $$\left( 1+{ m }^{ 2 } \right) \left( { x }^{ 2 }+{ y }^{ 2 }-{ a }^{ 2 } \right) +c\left( y-mx-c \right) =0$$
  • $$\left( 1+{ m }^{ 2 } \right) \left( { x }^{ 2 }+{ y }^{ 2 }-{ a }^{ 2 } \right) -2c\left( y-mx-c \right) =0$$
  • $$\left( 1+{ m }^{ 2 } \right) \left( { x }^{ 2 }+{ y }^{ 2 }-{ 2a }^{ 2 } \right) -2c\left( y-mx-c \right) =0$$
Three sides of a triangle have the equations $$L_{r} = y - m_r x - C_{r} = 0; r = 1, 2, 3$$. Then $$\lambda L_{2}L_{3} + \mu L_{3}L_{1} + \gamma L_{1}L_{2} = 0$$. where $$\lambda \neq 0, \mu \neq 0, \gamma \neq 0$$, is the equation of circumcircle of triangle if
  • $$\lambda (m_{2} + m_{3}) + \mu (m_{3} + m_{1}) + \gamma (m_{1} + m_{2}) = 0$$
  • $$\lambda (m_{2}m_{3} - 1) + \mu (m_{3}m_{1} - 1) + \gamma (m_{1}m_{2} - 1) = 0$$
  • Both $$(a)$$ and $$(b)$$ hold together
  • None of these
The equation of the circle passing through the points $$(4, 1), (6, 5)$$ and having the centre on the line $$4x+y-16=0$$ is 
  • $${ x }^{ 2 }+{ y }^{ 2 }-6x-8y+15=0$$
  • $$15({ x }^{ 2 }+{ y }^{ 2 })-94x+18y+55=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-4x-3y=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }+6x-4y=0$$
The length of latus rectum of the parabola $$4y^{2}+3x+3y+1=0$$ is 
  • $$\dfrac {4}{3}$$
  • $$7$$
  • $$12$$
  • $$\dfrac {3}{4}$$
Equation of the circle which is such that the lengths of the tangents to it from the points  $$( 1,0 ) , ( 0,2 )$$  and  $$( 3,2 )$$  are  $$1 , \sqrt { 7 }$$  and  $$\sqrt { 2 }$$  respectively is
  • $$6 \left( x ^ { 2 } + y ^ { 2 } \right) - 28 x - 5 y + 28 = 0$$
  • $$9 \left( x ^ { 2 } + y ^ { 2 } \right) - 28 x - 5 y + 28 = 0$$
  • $$3 \left( x ^ { 2 } + y ^ { 2 } \right) - 28 x - 5 y + 28 = 0$$
  • $$x ^ { 2 } + y ^ { 2 } -  x + y + 1 = 0$$
Which of the following is the equation of a circle?
  • $$x^2 + 2y^2 - x + 6 = 0$$
  • $$x^2 - y^2 + x + y + 1 = 0$$
  • $$x^2 - y^2 + xy + 1 = 0$$
  • $$3(x^2 + y^2) + 5x + 1 = 0$$
The latus rectum of an ellipse is a line 
  • Through a focus
  • Through the centre
  • Perpendicular to major axis
  • Parallel to minor axis
The equation to the circle which touches the axis of y at the origin and passes through $$(3, 4)$$ is?
  • $$2(x^2+y^2)-3x=0$$
  • $$3(x^2+y^2)-25x=0$$
  • $$4(x^2+y^2)-25y=0$$
  • $$4(x^2+y^2)-25x+10=0$$
The image of the circle $$(x - 3)^2 + (y - 2)^2 = 1$$ in the line mirror $$ax + by = 19$$ is $$(x - 1)^2 + (y - 16)^2 = 1$$ then values of (a, b) is
  • (1,1)
  • (1,1)
  • (1,1)
  • (-1,-1)
The radius of circle $$x^2+y^2-6x-8y=0$$
  • 5
  • 4
  • 3
  • 2
The equation of circle center at $$(0,0)$$ and Radius $$8cm$$
  • $$x^2+y^2=64cm$$
  • $$x^2+y^2=8$$
  • $$x^2+y^2=16$$
  • $$x^2+y^2=4$$
A circle of radius $$'5'$$ touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along the positive direction, then its equation in new position is 
  • $${x}^{2}+{y}^{2}-10(2\pi+1)x-10y+100{\pi}^{2}+100\pi+25=0$$
  • $${x}^{2}+{y}^{2}+10(2\pi+1)x-10y+100{\pi}^{2}+100\pi+25=0$$
  • $${x}^{2}+{y}^{2}-10(2\pi+1)x+10y+100{\pi}^{2}+100\pi+25=0$$
  • $${x}^{2}+{y}^{2}+10(2\pi+1)x+10y+100{\pi}^{2}+100\pi+25=0$$
If the circle $$x^{2}+y^{2}=9$$ passesthrough $$(2,c)$$ then $$c$$ is equal to 
  • $$\sqrt5$$
  • $$\sqrt 6$$
  • $$\sqrt 3$$
  • $$\sqrt 7$$
The equation of the circle of radius $$5$$ with centre on  x-axis and passing through the point $$(2,3)$$ is
  • $$x^{2}+y^{2}-12x+11=0$$
  • $$x^{2}+y^{2}-4x-21=0$$
  • $$x^{2}+y^{2}+12x+11=0$$
  • $$x^{2}+y^{2}-4x+21=0$$
The equation of the circle which touches the axis of y at a distance $$+4$$ from the origin and cuts off an intercept $$6$$ from the $$+ve$$ direction of x-axis is
  • $$x^{2}+y^{2}-10x\pm8y-16=0$$
  • $$x^{2}+y^{2}+10x\pm8y+16=0$$
  • $$x^{2}+y^{2}-10x\pm8y+16=0$$
  • $$x^{2}+y^{2}-8x\pm10y-16=0$$
The equation of the circle passing through the origin and making intercept $$4,5$$ on the positive coordinates axes is 
  • $$x^{2}+y^{2}-4x+5y=0$$
  • $$x^{2}+y^{2}-4x-5y=0$$
  • $$x^{2}+y^{2}+4x+5y=0$$
  • `$$x^{2}+y^{2}+4x-5y=0$$
The equation of the circle, the end points of whose diameter are the centre of the circles $$x^{2}+y^{2}+6x-14y=1$$ and $$x^{2}+y^{2}-4x+10y=2$$ is 
  • $$x^{2}+y^{2}+x-2y-14=0$$
  • $$x^{2}+y^{2}+x+2y-14=0$$
  • $$x^{2}+y^{2}+x+2y+14=0$$
  • $$x^{2}+y^{2}+x-2y=0$$
The equation of a circle with centre at $$(2,-3)$$ and the circumference is $$10 \pi$$ units is 
  • $$x^{2}+y^{2}+4x+6y+12=0$$
  • $$x^{2}+y^{2}-4x+6y-12=0$$
  • $$x^{2}+y^{2}-4x+6y+12=0$$
  • $$x^{2}+y^{2}-4x-6y-12=0$$
Equation having circle centre $$(5, 2)$$ and which passes through the point $$(1, -1)$$ is 
  • $$x^2+y^2-10x-4y-4=0$$
  • $$x^2+y^2+10x+4y+4=0$$
  • $$x^2+y^2-10x-4y-2=0$$
  • $$x^2+y^2-10x-4y+4=0$$
Equation of circle touching the line $$x + y = 4$$ at $$( 1, 3)$$ and intersecting the circle $${ x }^{ 2 }+{ y }^{ 2 }=4$$ orthogonally is
  • $${ x }^{ 2 }+{ y }^{ 2 }-x+2y-15=0$$
  • $${ x }^{ 2 }+{ y }^{ 2 }-x-y-6=0$$
  • $${ 2x }^{ 2 }+2{ y }^{ 2 }-x+y-22=0$$
  • $${ 2x }^{ 2 }+2{ y }^{ 2 }-x-9y+8=0$$
The parametric equation of the circle $$x^{2}+y^{2}+x+\sqrt {3}y=0$$ are
  • $$x=\dfrac{-1}{2}+\cos \theta,y=\dfrac {-\sqrt {3}}{2}+\sin\theta$$
  • $$x=-\dfrac {1}{2}+\cos \theta,y=\dfrac {\sqrt {3}}{2}+\sin\theta$$
  • $$x=\dfrac {1}{2}+\cos \theta,y=\dfrac {-\sqrt {3}}{2}+\sin\theta$$
  • $$x=\dfrac {1}{2}+\cos \theta,y=\dfrac {\sqrt {3}}{2}+\sin\theta$$
The equation $$\sqrt{(x-3)^{2}+(y-1)^{2}}+\sqrt{(x-3)^{2}+(y-1)^{2}}=6$$ represents : 
  • an ellipse
  • a pair of straight lines
  • a circle
  • the line segment joining the point $$(-3,1)$$ to the point $$(3,1)$$
If the line $$x-1=0$$ is the directrix of the parabola $${ y }^{ 2 }-kx+8=0$$, then one of the values of $$k$$ is 
  • $${ 1 }/{ 8 }$$
  • $$8$$
  • $$4$$
  • $${ 1 }/{ 4 }$$
The equation of the circle with centre at $$(4, 3)$$ and touching the line $$5x-12y-10=0$$ is?
  • $$x^2+y^2-4x-6y+4=0$$
  • $$x^2+y^2+6x-8y+16=0$$
  • $$x^2+y^2-8x-6y+21=0$$
  • $$x^2+y^2-24x-10y+144=0$$
The locus of center of a variable circle touching the circle of radius $${ r }_{ 1 }and{ r }_{ 2 }$$ extemally which also touch each other externally , is a conic of the eccentricity $$e$$.If $$\dfrac { { r }_{ 1 } }{ { r }_{ 2 } } =3+2\sqrt { 2 } $$ then $${ e }^{ 2 }$$ is 
  • 2
  • 3
  • 4
  • 5
The equation of the latus rectum of the parabola $$x^2 + 4x + 2y = 0$$ is-
  • 3y = 2
  • 2y + 3 = 0
  • 2y = 3
  • 3y + 2 = 0
If two vertices of an equilateral triangle are $$A (-a, 0)$$ and $$B(a, 0), a > 0$$ and the third vertex C lies above x-axis then the equation of the circumcircle of $$\Delta ABC$$ is
  • $$3x^2+3y^2-2\sqrt{3} ay =3a^2$$
  • $$3x^2+3y^2-2 ay =3a^2$$
  • $$x^2+y^2-2ay =a^2$$
  • $$x^2+y^2-\sqrt{3} ay =3a^2$$
The equation(s) of the circle(s) which pass through the ends of the common chords of two circles $$2x^{2}+2y^{2}+8x+4y-7=0$$ and $$x^{2}+y^{2}-8x-4y-5=0$$ and touch the line $$x=7$$ is (are) :
  • $$x^{2}+y^{2}-6x+2y-\dfrac{19}{4}=0$$
  • $$x^{2}+y^{2}+120x+60y+11=0$$
  • $$x^{2}+y^{2}-6x+2y+\dfrac{19}{4}=0$$
  • $$x^{2}+y^{2}+120x+60y-11=0$$
The equation of the circle which touches the axes of $$y$$ at the origin and passing through $$(3,4)$$ is
  • $$4(x^{2}+y^{2})-25x=0$$
  • $$3(x^{2}+y^{2})-25x=0$$
  • $$2(x^{2}+y^{2})-3x=0$$
  • $$4(x^{2}+y^{2})-25x=0$$
The value of k, such that the equation 
$$2x^{2}+2y^{2}-6x+8y+k=0$$ represent a point circle , is 
  • 0
  • 25
  • $$\frac {25}{2}$$
  • $$-\frac {25}{2}$$
$$If$$ $${y^2} - 2x - 2y + 5 = 0$$ is 
  • $$a\,\,circle\,with\,centre\,(1,1)$$
  • $$a\,\,parabola\,with\,\,vertex\,(1,2)$$
  • $$a\,parabola\,with\,directrix\,x = \frac{3}{2}$$
  • $$a\,parabola\,with\,directrix\,x = - \frac{1}{2}$$
If the radius of the circle $$x^{2}+y^{2}-18x-12y+k=0$$ be $$11$$ then k=
  • 34
  • 4
  • -4
  • 49
0:0:1


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