Chapter 12.3, Problem 53E

To determine

To find:

The steps needed to show in the derivation of the equation of the hyperbola which says the equation

$\sqrt{{\left(x+c\right)}^2+y^2}-\sqrt{{\left(x-c\right)}^2+y^2}=\pm 2a$

simplifies to

$\left(c^2-a^2\right)x^2-a^2{y}^2=a^2\left(c^2-a^2\right)$