Question

Find the constant sum for an ellipse with foci F1 (2, 0), F2 (-6, 0) and the point on the ellipse (2, 6).

Answer 1

I set up the problem like this:
√(2-2)^2+(0-6)^2+ √(-6-2)^2+(0-6)^2

Answer 2

Looks good to me so far. So then you simplify?

Answer 3

I simplified it to:
√0^2+-6^2+√-8^2+-6^2
√0+36+√64+36
√36+100
=√136
11.66

Answer 4

I agree with the first few steps up until
\( \sqrt{0 + 36} + \sqrt{64 + 36} = \sqrt{36 + 100} \)
Square roots do not combine by addition. They are essentially treated like exponents and can only combine when multiplied. \(\sqrt{a}\sqrt{b} = \sqrt{ab} \)

Answer 5

Instead, you have \( \sqrt{36} + \sqrt{100} \) which can be simplified right there because those are perfect squares underneath square roots.

Answer 6

Ok so it would be:
√36=6 + 10=√100
answer is 16?

Answer 7

That looks better to me, yes. :)

Answer 8

Thank you :) I appreciate the help

Answer 9

you're welcome!