Answer
$c^2 = b^2 -a^2$
Work Step by Step
We know that since the lines are perpendicular, the slopes are opposite reciprocals:
$m_1 = \frac{c}{b-a}$
$m_2 = \frac{c}{a+b}$
These must multiply to get -1, so:
$\frac{c^2}{(a+b)(a-b)}= -1 \\ c^2 = b^2 -a^2$
