If 3 x + 4 y = 12 2 is a tangent o the ellipse x 2 a 2 + y 2 9 = 1 for some a ∈ R , then the distance between the foci of the ellipse is

Question

If 3 x + 4 y = 12 2 is a tangent o the ellipse x 2 a 2 + y 2 9 = 1 for some a ∈ R , then the distance between the foci of the ellipse is, 2 7, 4, 2 5, 2 2

MARKS App · Accepted Answer

3 x + 4 y = 12 2 ⇒ 4 y = - 3 x + 12 2 ⇒ y = - 3 4 x + 3 2 Condition of tangency c 2 = a 2 m 2 + b 2 18 = a 2 ∙ 9 16 + 9 a 2 ∙ 9 16 = 9 a 2 = 16 a = 4 e = 1 - b 2 a 2 = 1 - 9 16 = 7 4 ∴ a e = 7 4 ∙ 4 = 7 ∴ Focus are ± 7 , 0 ∴ Distance between foci = 2 7

Search any question & find its solution

Looking for more such questions to practice?