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Conic Sections ...

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  • Question 1
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    Eccentricity of the hyperbola whose asymptotes are given by $$3x + 2y +5 = 0$$ and $$2x +3y+ 5 = 0$$ is

  • Question 2
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    If $$x=2+3\cos\theta$$ and $$y=1-3\sin\theta$$ represent a circle then the centre and radius is?

  • Question 3
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    Which of the following can be the equation of an ellipse?

  • Question 4
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    The graph of the conic $$x ^ { 2 } - ( y - 1 ) ^ { 2 } = 1$$ has one tangent line with positive slope that passes through the origin, the point of tangency being (a, b). Then Length of the latus rectum of the conic is

  • Question 5
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    Let PQ be a variable focal chord of the parabola $${ y }^{ 2 }=4ax$$ where vertex is A. Locus of, centre triangle APQ is a parabola $$'{ P }_{ 1 }'$$ Latus rectum of parabola $${ P }_{ 1 }$$ is 

  • Question 6
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    If S be the focus of a parabola and PQ be the focal chord,such that SP=3 and SQ = 6,then the length of latus rectum of the parabola is

  • Question 7
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    The equation of the image of the circle $${ \left( x-3 \right)  }^{ 2 }\quad +\quad { \left( y-2 \right)  }^{ 2 }\quad =1\quad in\quad the\quad mirror\quad x+y=19\quad is$$

  • Question 8
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    If eccentricity of the hyperbola $$\dfrac {x^{2}}{\cos^{2}\theta}-\dfrac {y^{2}}{\sin^{2}\theta}=1$$ is more then $$2$$ when $$\theta\ \in \ \left(0,\dfrac {\pi}{2}\right)$$. Find the possible values of length of latus rectum 

  • Question 9
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    Let$$0<\theta <\dfrac { \pi  }{ 2 } .$$ If the eccentricity of the hyperbola $$\dfrac { { x }^{ 2 } }{ { cos }^{ 2 }\theta  } -\dfrac { { y }^{ 2 } }{ { sin }^{ 2 }\theta  } =1$$ is greater than 2, then the length of its latus rectum lies in the interval:

  • Question 10
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    Axes are coordinates axes, the ellipse passes through the points where the straight line $$\dfrac {x}{4}+\dfrac {y}{3}=1$$  meets the coordinates axes. Then equation of the ellipses is 

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