Question

PLEASE HELP MEDAL:

Find the Equation of an Ellipse with given Foci and Vertices

Vertices: (-2,-1). (-12, -1)
Foci: (-4, -1), (-10, -1)

Answer 1

please see the example:
Write an equation for the ellipse with vertices (4, 0) and (–2, 0)
and foci (3, 0) and (–1, 0).

The center is midway between the two foci, so (h, k) = (1, 0), by the Midpoint Formula. Each focus is 2 units from the center, so c = 2. The vertices are 3 units from the center, so a = 3. Also, the foci and vertices are to the left and right of each other, so this ellipse is wider than it is tall, and a2 will go with the x part of the ellipse equation.

The equation b2 = a2 – c2 gives me 9 – 4 = 5 = b2, and this is all I need to create my equation:

((x - 1)^2) / 9 + y^2 / 5 = 1