Question

Write an equation for the ellipse that satisfies the conditions: I got that the center is (-2,4), but I can't find the values of a or b.

15. endpoints of major axis (-8, 4) and (4, 4) and foci ( -3, 4) and ( -1, 4)

Answer 1

I love these!!! I will help you!

Answer 2

thank you that means a lot

Answer 3

An ellipse has a general form of \[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{b ^{2} }=1\]or\[\frac{ y ^{2} }{ a ^{2} }+\frac{ x ^{2} }{ b ^{2} }=1\]Since your major vertices are on the x axis, it is of the form of the first one up there.

Answer 4

a^2 is ALWAYS bigger than b^2, so the a^2 goes under the major vertex and the b^2 goes under the minor.

Answer 5

Let's start with the general form and the center, which you already said was (-2,4). That fits in the equation like this:

Answer 6

\[\frac{ (x+2)^{2} }{ a ^{2} }+\frac{ (y-4)^{2} }{b ^{2} }=1\]

Answer 7

If you draw that out roughly on a graph, it looks something like this:

Answer 8

Count the number of units that the center is from the endpoint. This is your a:Square that a and you get your first unknown...a^2. Fit it in now to the equation.