ellipse, please help to solve this one, thank you

Question

An ellipse has endpoints of its axes at the points  and . Give the equation of the ellipse.

Answer 1

The standard equation for an ellipse is ^{(x - h)²} / _a² + ^{(y - k)²} / _b² = 1

where horizontal radius = a, vertical radius = b and center = (h, k)

We are given end points of the axes:

horizontal axis (because y coordinate is same) is (-12, -8) to (2, -8)

=> x diff = 2 - -12 = 14 => a = 14/2 = 7 and h = -12 + 7 = -5

vertical axis (because x coordinate is same) is (-5, -13) to (-5, -3)

=> y diff = -3 - -13 = 10 => b = 10/2 = 5 and k = -13 + 5 = -8

hence equation is (x - -5)² / 7² + (y - -8)² / 5² = 1

=> (x + 5)² / 49 + (y + 8)² / 25 = 1 or 25(x + 5)² + 49(y + 8)² = 1225, if you prefer

You can double-check the points and equation on Desmos Graphing or similar.