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in Mathematics by (53.3k points)

Let S = (1, 2) and S' = (5, 5) be the foci of a hyperbola. For any point P on the curve, it is given that |S'P - SP| = 3. If e' is the eccentricity of the conjugate hyperbola, then 4e' is equal to .......

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Best answer

we have

|S'P - SP| = 3 ⇒ 2a = 3 or a = 3/2

Therefore

2ae = SS' = 5 ⇒ 3e = 5 ⇒ e = 5/3

Hence

1/e2 + 1/e'2 = 1

⇒ 1/e'2 = 1 - 1/e2 = 1 - 9/25 = 16/25

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