Question

Find the constant difference for a hyperbola with foci at F1 (0, -10) and F2 (0, 10) and the point on the hyperbola (6, 7.5)

Answer 1

So I plugged in the numbers for the formula |√x1-x3)^2+(y1-y3)^2 -√(x2-x3)^2+(y2-y3)^2|
Which would be:
|√0-6)^2+(-10-7.5)^2 -√(0-6)^2+(10-7.5)^2|

Answer 2

that's correct

Answer 3

Ok so when I simplified the problem it looks like this:
√-6^2+-17.5^2 - √-6^2+2.5^2

Answer 4

\(\bf (0-6)^2\implies (-6)^2\implies -6\cdot -6\implies +36\)

Answer 5

So then I got √36+306.25 - √36+6.25

Answer 6

yeap

Answer 7

Which would end up as -16.439-42.25
It doesn't look right I don't think it is the answer

Answer 8

-58.689 ?

Answer 9

well \(\bf \sqrt{(0-6)^2+(-10-7.5)^2}-\sqrt{(0-6)^2+(10-7.5)^2}
\\ \quad \\
\sqrt{(-6)^2+(-17.5)^2}-\sqrt{(-6)^2+(-2.5)^2}
\\ \quad \\
\sqrt{36+306.25}-\sqrt{36+6.25}
\\ \quad \\
\sqrt{342.25}-\sqrt{42.25}\)

Answer 10

18.5-6.5=12

Answer 11

yeap

Answer 12

Thank you! I appreciate your help

Answer 13

yw