I can see it now...

Syllybus for Pre-Algebra:

1) How to do stuff for tests.

2) Where to plug stuff in.

That is a fine course.

Distance from (-3,0) is $\displaystyle \sqrt{(x-(-3))^{2}+(y-0)^{2}}$

Simplify a bit $\displaystyle \sqrt{(x+3)^{2}+y^{2}}$

Distance from (3,0) is $\displaystyle \sqrt{(x-3)^{2}+(y-0)^{2}}$

Simplify a bit $\displaystyle \sqrt{(x-3)^{2}+y^{2}}$

Twice the Distance

$\displaystyle \sqrt{(x+3)^{2}+y^{2}} = 2\cdot \sqrt{(x-3)^{2}+y^{2}}$

Everything is positive, so there is no harm in squaring both sides.

$\displaystyle (x+3)^{2}+y^{2} = 4\cdot ((x-3)^{2}+y^{2})$

Now what?