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The vertices of the triangle A B C are A 0,0 ,   B 3 , 0 and C 3 , 4 , where A and C are foci of an ellipse and B lies on the ellipse. If the length of the latus rectum of the ellipse is 12 p units, then the value of p is

Correct answer

3.5

Step-by-step solution

A C = 5 = 2 a e ⇒ 2 a e = 5 … i Also A B + B C = 2 a ⇒ 2 a = 7 ⇒ a = 7 2 ∴ e = 5 7 ⇒ 1 - b 2 a 2 = 25 49 ⇒ b = 6 Length of the latus rectum, 2 b 2 a = 2 × 6 7 2 units ⇒ p = 7 2 = 3 .5

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