Hello, Hockey_Guy14!

If you're having trouble with ellipses,

. . perhaps you don't understand the basic concepts.

But I must admit: this problem can be somewhat tricky.

Find an equation for the ellipse centered at the origin

with one focus (0,-3) and the sum of the focal radii equal to 10. Sketch.

An ellipse centered at the origin has the equation: .

where is the "x-radius" and is the "y-radius".

is the "focal distance", distance from the center to a focus.

. . Formula: .

Since one focus is (0,-3), the other is (0,3) . . . and

We also know that the ellipse is "horizontal": . Code:

b|
* * * P
* | *
* | * * *
* * * *
* | *
* - - * - - - + - - - * - - *
F2 | F1 a

The "focal radii" are the distances

. . We are told that: .

Here's a lesser-used fact: .

. . The sum of the focal radii is twice the semimajor axis.

So we have:. .

From the formula, we have: .

Therefore, the equation is: .