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Example 4 of how to find the equation of a hyperbola

A hyperbola has the same focus as an ellipse. An ellipse has the equation x2/64 + y2/15 = 1. The asymptotes of the hyperbola is y = +- (3/4) x. Find the equation for the hyperbola.

From an ellipse equation, we know its major axis, minor axis and coordinate of the focus. For a hyperbola, know the focus and asymptotes, we have the equation between the half real axis and half imaginary axis, which are two unknown variables. We need another equation to solve these two variables. The equation is that the square of the focus is equal to the sum of the square of the half major axis and the square of the half minor axis. Know the half major axis and the half minor axis, we can write the equation for the hyperbola.