Question

The equation of the hyperbola whose eccentricity is $\frac{5}{4}$, where focus is $(a,0)$ and whose directrix is $4x-3y=a$ is $7y^2+24xy-24ax-16ay+15a^2=0$

• A. True
• B. False

Answer 1

The correct option is A True

By definition, the equation of hyperbola having focus $(a,0)$ and directrix as $4x-3y=a$ and eccentricity $\frac{5}{4}$ will be

$(x-a{)}^2+(y-0{)}^2=(\frac{5}{4}{)}^2|\frac{4x-3y-a}{\sqrt{4^2+3^2}}{|}^2$

$16(x^2-2ax+a^2+y^2)=16x^2+9y^2+a^2-24xy-8ax+6ay$

$7y^2+24xy-24ax-16ay+15a^2=0$