## GiggleSquid 3 years ago One focus is at (5,-11.94). Find the other focus for the ellipse defined by this equation: (x-5)^2/1 + (y+4)^2/64=1

1. telliott99

The ellipse is centered at 5,-4 The minor axis is 2a with a = 1 The major axis is 2b with b = sqrt(64) = 8. Have to look up for the foci again.

2. GiggleSquid

so the major axis is 2 x 8 or is it just 8, thanks for the help btw

3. telliott99

The foci are at sqrt(b^2 - a^2) = 7.937, have to compute the offsets based on the origin.

4. telliott99

I think the terminology is major axis = 2 x 8 semi-major axis = 8

5. telliott99

study up :) http://en.wikipedia.org/wiki/Ellipse

6. GiggleSquid

:/

7. GiggleSquid

so how do i get the y value for the foci, the x being 7.937 right?

8. telliott99

Offsets: foci are at x = 5 y-values are -4 +/- 7.937 = -11.937, 3.937

9. telliott99

This ellipse has its long dimension vertical.

10. GiggleSquid

so its -11.937,3.937?

11. telliott99

Those are the y's. (5,-11.937) and (5,3.937)

12. telliott99

Maybe I didn't say that clearly. Because the ellipse is oriented vertically (y stretched more), the foci have the same x-value, which is equal to the origin, 5. The foci are +/- sqrt(63) see above with respect to the y-value of the origin, which is -4, so that gives what I said.