In the standard ellipse x²/a² + y²/b² = 1 (with a b), the relationsh…

Question

In the standard ellipse x²/a² + y²/b² = 1 (with a > b), the relationship between a, b, c (focal distance) is:

Accepted Answer

D. $a^2 = b^2 + c^2$ (semi-major related)

ELLIPSE: a² = b² + c². So b² = a² − c² + c² = a² − ... actually: b² = a²(1−e²); c² = a²e². → a² = b² + c². HYPERBOLA: c² = a² + b² (note difference). Foci at (±c, 0) in both.

Answer

$a^2 = b^2 - c^2$ (subtraction)

Answer

$c^2 = a^2 + b^2$ (hyperbola formula)

Answer

$a^2 + b^2 = c^2$ (Pythagorean type)