Chapter 11.3, Problem 54E

(a)

To determine

The values of $a$, $b$ and $c$, and find the foci $F_1\text{and}{F}_2$ for the hyperbola $\frac{x^2}{9}-\frac{y^2}{16}=1$.

(b)

To determine

To show: The point $P\left(5,\frac{16}{3}\right)$ lie on this hyperbola, $\frac{x^2}{9}-\frac{y^2}{16}=1$.

(c)

To determine

To find: The distances $d\left(P,F_1\right)$ and $d\left(P,F_2\right)$.

(d)

To determine

To verify: The difference between $d\left(P,F_1\right)$ and $d\left(P,F_2\right)$ is $2a$.