IIT JEE 1983 Maths - 'Adapted' - FIB to Single-Digit Integer Q2

Given the points $A(0,4)$ and $B(0, -4)$ , the equation of the locus of the points $P(x,\ y)$ such that $|AP-BP|=6$ is $\dfrac{x^2}p - \dfrac{y^2}{q} = r$ where $p,q\in\mathbb R^+$ and $\lvert r\rvert=1$ . Find $\left\lfloor \frac{p+q+2r}5 \right\rfloor$ .

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .