Problems Involving Conic Sections

Question

Find the standard equation of the ellipse whose major and minor axes are the transverse and conjugate axes (not necessarily in that order) of the hyperbola

y ² -x² -4x-4y-4=0.

Answer 1

Completing squares standard equation of hyperbola: (y - 2)²/4 - (x + 2)²/4 = 1.

Center of hyperbola is (- 2, 2); a = 2 and b = 2. So, ellipse: (x + 2)²/8 + (y - 2)²/4 = 1