Compute some properties of ellipses and hyperbolas

by RoRi

May 31, 2016

Let $p$ be a positive number. Then the equation $px^2 + (p+2)y^2 = p^2 + 2p$ is the equation of an ellipse. Find (in terms of $p$ ) the eccentricity and the foci of this ellipse.
Find a Cartesian equation for the hyperbola with the same foci as in part (a) and which has eccentricity $e = \sqrt{3}$ .

Incomplete.

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