Question

If length of transverse axis is 8 and conjugate axis is 10 and transverse axis is along x-axis then find the equation of hyperbola.

(a) \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1

(b) \((\frac{x}{5})^2-(\frac{y}{4})^2\)=1

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

(d) \((\frac{x}{8})^2-(\frac{y}{10})^2\)=1

I got this question in exam.

Query is from Conic Sections topic in division Conic Sections of Mathematics – Class 11

Answer 1

Right answer is (a) \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1

Easiest explanation: Given, 2a=8 => a=4 and 2b=10 => b=5.

Equation of hyperbola with transverse axis along x-axis is \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1.

So, equation of given hyperbola is \((\frac{x}{4})^2-(\frac{y}{5})^2\)=1.