Question

Equation of the hyperbola with length of the latusrectum $\frac{9}{2}$ and e = $\frac{5}{4}$ is

• A. $\frac{x^z}{45}-\frac{y^z}{36}=1$
• B. $\frac{x^z}{16}-\frac{y^z}{45}=1$
• C. $\frac{x^z}{16}-\frac{y^z}{32}=1$
• D. $\frac{x^z}{16}-\frac{y^z}{9}=1$

Answer 1

The correct option is D

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

$\frac{2b^z}{a}=\frac{9}{2}$ e = $\frac{5}{4}$ $b^2$ = 16 $(\frac{25}{16}-1)$ = 9

$\Rightarrow$ $4b^2=9a$ $\Rightarrow$ $\frac{x^z}{16}-\frac{y^z}{9}=1$

$\Rightarrow$ $4a^2(e^2-1)=9a$

$\Rightarrow$ 4a $\left(\frac{9}{16}\right)=9$

$\Rightarrow$ a = 4