Find an equation for the ellipse.

Question

Find an equation for the ellipse.

Foci at (0,4) and (0,-4); length of major axis is 14.

I would really like help figuring this equation out. Even if you prefer to use different but similar numbers to help me understand how to work the equation works too. I'm struggling in math and I really want to understand it before exams start. Even the textbook explanation just wasn't clicking for me.

Please and thank you for your assistance,

Answer 1

As the foci are at (0, 4) and (0, -4), the ellipse is centered at ((0+0)/2,(4+-4)/2) = (0, 0)

The distance from the foci to the center is 4. The distance from the center to the end of the major axix is 14/2 = 7

From 7 and 4, we use the formula to get the distance to the minor axis end sqrt(7^2-4^2) = sqrt(49-16) = sqrt(33)

We now have what we need to describe the ellipse from the center (0, 0) and the distance to the end of the axes sqrt(33) and 7

x^2/33 + y^2/49 = 1