Question

If the latus rectum of an hyperbola be 8 and eccentricity be $\frac{3}{\sqrt{5}}$ , then the equation of the hyperbola is

• A. $4x^2-5y^2=100$
• B. $5x^2-4y^2=100$
• C. $4x^2+5y^2=100$
• D. $5x^2+4y^2=100$

Answer 1

The correct option is A

$4x^2-5y^2=100$

$\frac{2b^2}{a}=8and\frac{3}{\sqrt{5}}=\sqrt{1+\frac{b^2}{a^2}}or\frac{4}{5}=\frac{b^2}{a^2}$
$\Rightarrow a=5,b=2\sqrt{5}$.
Hence the required equation of hyperbola is $\frac{x^2}{25}-\frac{y^2}{20}=1\Rightarrow 4x^2-5y^2=100$.