Let the curve C be the mirror image of the parabola y 2 = 4 x with respect to the line x + y + 4 = 0 . If A and B are the points of intersection of C with the line y = - 5 , then the distance between

Question

Let the curve C be the mirror image of the parabola y 2 = 4 x with respect to the line x + y + 4 = 0 . If A and B are the points of intersection of C with the line y = - 5 , then the distance between A and B is

TestHub · Accepted Answer

Equation of AA ′ is y + 5 = 1 x - α ⇒ y = x - α - 5 y - x = - α - 5 ...(i) Also x + y = - 4 y = - α - 9 2 2 x = α + 1 ⇒ x = α + 1 2 M ≡ α + 1 2 , - α - 9 2 A ′ = 1 , α - 4 A ′ lies on parabola Now, α 2 + 16 + 8 α = 4 ⇒ α 2 + 8 α + 12 = 0 ⇒ α = - 2 , - 6 AB = distance = 4 units

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