Find the standard form of the equation of the ellipse with the given characteristics. foci: (-5,-12), (-5,-4), endpoints of the major axis: (-5,-16), (-5,0)

Question

Find the standard form of the equation of the ellipse with the given characteristics.

foci: (-5,-12), (-5,-4), endpoints of the major axis: (-5,-16), (-5,0)

Answer 1

Center is (- 5, (- 16 + 0)/2) = (-5, -8); 2a = 0 - (-16) = 16; a = 8; 2c = - 4 - (-12) = 8; c = 4; b² = 64 - 16 = 48.

Equation of ellipse: (x + 5)²/48 + (y + 8)²/64 = 1