How can I rearrange this formula?

[poloshermanos]

Homework Statement

Hi!

I'm reading a great book by Paul Nahin, 'Chases & Pursuits', and during one derivation he skips a few steps in rearranging a formula. I'm struggling to see exactly how it was arranged and it's really bugging me.. it can't be too difficult, I think I'm just missing a key step in the process.

If someone would be kind enough as to give me a clue it would be much appreciated!

Thanks in advance,
Gus

Homework Equations

$\frac{\sqrt{(x-a)^{2}+y^{2}}}{\sqrt{(x-b)^{2}+y^{2}}}=k^{2}$

where $a$, $b$ and $k$ are constants.

The Attempt at a Solution

(or 'What it should be rearranged to')

$\left [ x-\frac{k^{2}b-a}{k^2-1}\right ]^{2}+y^{2}=\left [\frac{k(a-b)}{1-k^{2}}\right ]^{2}$

 

[SteamKing]

What are p and m?

 

[poloshermanos]

Apologies, I wanted to change p and m from the original text to a and b... OP has been updated.

 

[SammyS]

...
If someone would be kind enough as to give me a clue it would be much appreciated!

Thanks in advance,
Gus

Homework Equations

$\frac{\sqrt{(x-a)^{2}+y^{2}}}{\sqrt{(x-b)^{2}+y^{2}}}=k^{2}$

where $a$, $b$ and $k$ are constants.

The Attempt at a Solution

(or 'What it should be rearranged to')

$\left [ x-\frac{k^{2}b-a}{k^2-1}\right ]^{2}+y^{2}=\left [\frac{k(a-b)}{1-k^{2}}\right ]^{2}$

Start by multiplying both sides by the denominator. Then square both sides. ...