Geometry
# Conic Sections

What are the coordinates of the foci of the rectangular hyperbola $x^2-y^2=7 ^2?$

What are the coordinates of the vertices of the hyperbola $4x^2-9y^2-40x+54y -17=0 ?$

Given points $F=(5,0)$ and $F'=(-5,0),$ what is the equation of the locus of points $P$ in a plane such that $\left\lvert \left\lvert \overline{PF} \right\rvert - \left\lvert \overline{PF'} \right\rvert \right\rvert= 8 ?$

Note: $\lvert \overline{AB} \rvert$ denotes the length of line segment $\overline{AB}.$