Question

The equation of a hyperbola whose asymptotes are $3x \pm 5y = 0$ and vertices are $( \pm 5, 0)$ is

• A. $3x^2-5y^2=25$
• B. $5x^2 - 3y^2 = 225$
• C. $25x^2-9y^2=225$
• D. $9x^2 -25y^2 =225$

Answer 1

Answer: (D)

The given equation of asymptotes of hyperbola is
$3 x \pm 5 y=0$...(i)
and vertices $(\pm 5,0)$
Now, equation of hyperbola is
$(3 x+5 y)(3 x-5 y)=\lambda$
$9 x^{2}-25 y^{2}=\lambda$...(ii)
Since, $(\pm 5,0)$ is the vertices of the hyperbola, then
$9(5)^{2}-0=\lambda \Rightarrow \lambda=225$
From Eq. (ii), $9 x^{2}-25 y^{2}=225$