Question

Find the constant sum for an ellipse with foci F1 (3, 0), F2 (24, 0) and the point on the ellipse (9, 8)

Answer 1

Compute the distance from F1 to P(9,8) on the ellipse and add it to the distance from F2 to P(9,8) on the ellipse.

Answer 2

The sum notion originates from the definition of an ellipse as the set of points in a plane, the sum of whose distance from two fixed points (foci) is a constant greater than the distance between them (the foci).

Answer 3

So just use use the distance formula for the ellipse and then add the two square roots?

Answer 4

Yes.
What is the distance from F1 (3, 0) to (9, 8) ?
You crank it out and I will, too.

Answer 5

Then, this:
F2 (24, 0) to (9, 8)

Answer 6

I'm ready to compare when you are @MawellMcNulty

Hey, if you know how to do the distance formula by hand, then use technology as well.

Use the distance between two points calculator at this URL:
http://easycalculation.com/analytical/distance.php

Answer 7

For my final answer, the constant sum equals 27

Answer 8

10 + 17. Yes, that is what I got.

Answer 9

I got those distances aswell