Let there are exactly two points on the ellipse x 2 a 2 + y 2 b 2 = 1 whose distances from 0,0 are equal to a 2 2 + b 2 . Then, the eccentricity of the ellipse is equal to

Question

Let there are exactly two points on the ellipse x 2 a 2 + y 2 b 2 = 1 whose distances from 0,0 are equal to a 2 2 + b 2 . Then, the eccentricity of the ellipse is equal to, 1 2, 1 2 2, 1 2, None of these

MARKS App · Accepted Answer

Since, a 2 2 + b 2 > b Hence, major axis = 2 a & minor axis = 2 b and a 2 2 + b 2 = a ⇒ a 2 2 + b 2 = a 2 ⇒ b 2 = a 2 2 ⇒ b 2 a 2 = 1 2 ⇒ 1 - e 2 = 1 2 ⇒ e 2 = 1 2 = e = 1 2

Search any question & find its solution

Looking for more such questions to practice?