Question

If length of major axis is 10 and minor axis is 8 and major axis is along x-axis then find the equation of ellipse.

(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

The question was posed to me in an interview for job.

This interesting question is from Conic Sections topic in portion Conic Sections of Mathematics – Class 11

Answer 1

The correct choice is (b) \((\frac{x}{5})^2+(\frac{y}{4})^2\)=1

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

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

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