Question

If foci of an ellipse are (0, ±3) and length of semimajor axis is 5 units, 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

I have been asked this question in final exam.

I would like to ask this question from Conic Sections topic in portion Conic Sections of Mathematics – Class 11

Answer 1

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

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

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

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