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JEE Main202225 Jun 2022Evening ShiftMathematicsHyperbolaActual

Let the eccentricity of the hyperbola x 2 a 2 - y 2 b 2 = 1 be 5 4 . If the equation of the normal at the point 8 5 , 12 5 on the hyperbola is 8 5 x + β y = λ , then λ - β is equal to _____.

Correct answer

0

Step-by-step solution

Using the formula of eccentricity we get, e 2 = 1 + b 2 a 2 = 25 16 ⇒ b 2 a 2 = 9 16           . . . 1 A 8 5 , 12 5 satisfies x 2 a 2 - y 2   b 2 = 1 ⇒ 64 5 a 2 - 144 25   b 2 = 1           . . . 2 Solving 1   &   2 b = 6 5 a = 8 5 Normal at A is 5 a 2 x 8 + 5   b 2 y 12 = a 2 + b 2 Comparing it 8 5 x + β y = λ Gives λ = 100 , β = 15 So, λ - β = 85

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