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An ellipse E has the equation (x^(2))/(3...

An ellipse E has the equation `(x^(2))/(36) + (y^(2))/(32) = 1` and C and S are its centre and a focus the usual notation. A hyperbola H has a vertex at C, point S as its focus nearer to C and latus rectum of equal length to that of E. Show that H has the eccentricity `(5)/(3)` and find its equation

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The correct Answer is:
`16x^(2) - 9y^(2) + 96x = 0`
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