Question

Equation of the hyperbola with foci (0,± 5) and e = $\frac{5}{3}$ is

• A. $\frac{y^z}{9}-\frac{y^z}{16}=1$
• B. $\frac{x^z}{16}-\frac{y^z}{9}=1$
• C. $\frac{x^z}{16}-\frac{y^z}{9}=1$
• D. $\frac{x^z}{12}-\frac{y^z}{13}=1$

Answer 1

The correct option is B

$\frac{x^z}{16}-\frac{y^z}{9}=1$

Foci = ( 0 , ±5 ) = ( 0 , ± be)

b$\frac{5}{3}$ = 5 $\Rightarrow$ b = 3

$a^2=9(\frac{25}{9}-1)$ = 16

$\frac{x^2}{16}-\frac{y^2}{9}=-1$