Question

If foci of a hyperbola are (0, ±5) and length of semi transverse axis is 3 units, then find the equation of hyperbola.

(a) \((\frac{x}{4})^2-(\frac{y}{3})^2\)=1

(b) \((\frac{x}{3})^2-(\frac{y}{4})^2\)=1

(c) \((\frac{x}{10})^2+(\frac{y}{8})^2\)=1

(d) \((\frac{x}{8})^2-(\frac{y}{6})^2\)=1

I got this question during an interview.

This intriguing question comes from Conic Sections topic in section Conic Sections of Mathematics – Class 11

Answer 1

Right answer is (a) \((\frac{x}{4})^2-(\frac{y}{3})^2\)=1

Explanation: Given, a=3 and c=5 => b^2=c^2-a^2 = 5^2-3^2=4^2 => b=4.

Equation of hyperbola with transverse axis along y-axis is \((\frac{y}{a})^2-(\frac{x}{b})^2\)=1.

So, equation of given hyperbola is \((\frac{y}{3})^2-(\frac{x}{4})^2\)=1.