Question

The latus rectum of an ellipse is 10 and the minor axis is equal to the distance between the foci. The equation of the ellipse is

• A. x² + 2y² = 100
• B. x² + $\sqrt{2}$y² = 10
• C. x² – 2y² = 100
• D. None of these

Answer 1

Answer: (A)

x² + 2y² = 100

Answer 2

Given $\frac{2b^{2}}{a}$= 10 and 2b = 2ae

Also b² = a² (1 – e²) ⇒ e² = (1 – e²) ⇒ e = $\frac{1}{\sqrt{2}}$

⇒ b = $\frac{a}{\sqrt{2}}$or b = 5$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$, a = 10

Hence equation of ellipse is $\frac{x^{2}}{(10)^{2}} + \frac{y^{2}}{\left( 5\sqrt{2} \right)^{2}}$ = 1

i.e., x² + 2y² = 100.