Question

If minor axis of an ellipse is equal to the distance between foci and length of latus rectum is 10, the equation of the ellipse will be-

• A. 16x² + 20y² = 625
• B. x² + 2y² = 100
• C. 16x² + 20y² = 1
• D. 2x² + y² = 50

Answer 1

Answer: (B)

x² + 2y² = 100

Answer 2

$\frac{2b^{2}}{a}$ = 10 ......(i) ; 2b = 2ae .....(ii)

2b = 2ae ̃ b² = a²e² ̃ a²(1–e²)=a²e² ; 2e² = 1

e = $\frac{1}{\sqrt{2}}$

$\frac{2b^{2}}{a}$ = 10 ̃ b² = 5a ̃ a²(1–$\frac{1}{2}$) = 5a

$\frac{a}{2}$ = 5 ̃ a = 10 , b² = 50

̃$\frac{x^{2}}{100}$+$\frac{y^{2}}{50}$=1̃x²+2y² = 100