Let the product of the focal distances of the point P(4, 2√3) on the hyperbola x^2/a^2-y^2/b^2 = 1 be 32.

Question

Let the product of the focal distances of the point \(P(4, 2\sqrt3)\) on the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) be 32. The length of conjugate axis be p and the length of it′s latus rectum be q. Then \(p^2+q^2\) is equal to ______.   

Answer 1

Answer is: 120 

\(P(4, 2\sqrt3) \equiv P(x_1, y_1)\)  

Solving (ii) & (iii)  

= 48 + 72 = 120