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utkarshakash
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Homework Statement
Through a given point in the plane of an ellipse prove that exactly two conics (one eliipse and the other hyperbola) confocal with the given ellipse can be drawn.
Homework Equations
The Attempt at a Solution
Let the equation of given ellipse be
[itex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2} = 1 [/itex]
The equation of confocals with this ellipse is
[itex] \dfrac{x^2}{a^2+\lambda}+\dfrac{y^2}{b^2+\lambda} = 1 [/itex]
Let the given point be (α,β).
But I have no idea how to proceed now? Should I substitute the given point in the equation to the confocals?