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

The intercept on the line y=x by the circle x2+y22x=0 is AB. The equation of the circle with AB as a diameter, is
  • x2+y2+x+y=0
  • x2+y2=x+y
  • x2+y23x+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 x2y=0 is
  • x2+y2x+7y=0
  • x2+y2+x7y=0
  • x2+y2x7y=0
  • x2+y2+x+7y=0
Length of the latus rectum of the parabola 25[(x2)2+(y3)2]=(3x4y+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
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