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If a tangent of slope 2 of the ellipse x 2 a 2 + y 2 1 = 1 passes through the point - 2,0 , then the value of a 2 is equal to

Correct answer

3.75

Step-by-step solution

A tangent of slope 2 to the ellipse x 2 a 2 + y 2 1 = 1 is y = 2 x ± 4 a 2 + 1 Since, it passes through - 2,0 ⇒ 0 = 2 - 2 ± 4 a 2 + 1 ⇒ 4 a 2 + 1 = 16 ⇒ a 2 = 15 4 = 3.75

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