The focal chord of y 2 = 64 x is tangent to x - 4 2 + y - 2 2 = 4 , then the square root of the length of this focal chord is equal to

Question

The focal chord of y 2 = 64 x is tangent to x - 4 2 + y - 2 2 = 4 , then the square root of the length of this focal chord is equal to, 74 9, 37 3, 74 3, 37 9

MARKS App · Accepted Answer

Let, the equation of the focal chord is y = m x - 16 Since the chord is tangent to the given circle ∴ 2 = 4 m - 16 m - 2 1 + m 2 ⇒ 4 1 + m 2 = - 12 m - 2 2 ⇒ m = 0 or - 12 35 ⇒ tan ⁡ θ = 12 35 ⇒ cosec ⁡ θ = 37 12 ⇒ Length of the focal chord, L = 64 × 37 12 2 units ⇒ The required value, L = 8 × 37 12 = 74 3

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