The equation x^22- - y^2 -5-1=0 represents an ellipse if

Correct answer: D. (d) : If x^22- - y^2 -5=1 represents an ellipse then 2- >0 and -5<0 ⇒ <2 and <5 ⇒ <2.

JEE Previous Year Question

$The equation \frac{x ^{2}}{2 - λ} - \frac{y ^{2}}{λ - 5} - 1 = 0 represents an ellipse if$

Topic: JEE PYQ

Answer: D. Full step-by-step solution below.

Correct answer: D

(d) : If \frac{x ^{2}}{2 - λ} - \frac{y ^{2}}{λ - 5} = 1 represents an ellipse then 2 - λ > 0 and λ - 5 < 0 \Rightarrow λ < 2 and λ < 5 \Rightarrow λ < 2 .