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Conic Sections ...

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  • Question 1
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    A circle has the same center as an ellipse and passes through the foci $${ F }_{ 1 }$$, and $${ F }_{ 2 }$$, of the ellipse, such that the two curves intersect in 4 points.Let "P' be any one of their point of intersection. If the major 17 triangle $$P F _ { 1 } F _ { 2 }$$ is $$30 ,$$ then the distance between the foci is _______________.

  • Question 2
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    From a point P perpendiculars PM and PN are drawn to curve $$3x^2+4xy+y^2=0$$ to meet at M and N. If MN$$=2\sqrt{5}$$, then?

  • Question 3
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    Equation of the latus rectum of the hyperbola $$(10x - 5)^{2} + (10y - 2)^{2} = 9(3x + 4y - 7)^{2}$$ is

  • Question 4
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    If the equation $$\frac { \lambda ( x + 1 ) ^ { 2 } } { 3 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$$ represents a circle then $$\lambda =$$

  • Question 5
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    The area enclosed between the parabolas $$y^2 = 4x$$ and $$x^2 = 4y$$ is

  • Question 6
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    Equation of the curve passing through the point $$(1,\ 2)$$ such that the intercept on the $$x-$$axis cut off between the tangent and origin is twice the abscissa is given by:

  • Question 7
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    Let $$S$$ and $$S ^ { 1 }$$ are the foci of an ellipse whose eccentricity is $$\frac { 1 } { \sqrt { 2 } } , B$$ and $$B ^ { 1 }$$ are the ends of minor axis then $$S B S ^ { \prime } B ^ { 1 }$$ forms $$a$$ ________________.

  • Question 8
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    $$D.E$$ of the curve for which the initial ordinates of any tangent is equal to the corresponding number 

  • Question 9
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    ABCD is a square of side 1 unit. A circle passes through vertices A,B of the square and the remaining two vertices of the square lie out side the circle. The length of the tangent draw to the circle from vertex D is 2 units. The radius of the circle is 

  • Question 10
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    The coordinates of the foci of the hyperbola $$xy=c^2$$ are 

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