If the reflection of the parabola $y^{2} = 4 (x - 1)$ in the line x + y = 2 is the curve $A x + B y = x^{2}$ , then the value of (A+B) is

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Solution

The correct option is A
0

Let a variable point on the parabola be $(1 + t^{2}, 2 t)$ and its reflection in the given line be (h, k)

$∴ h - (1 + t)^{2} = k - 2 t = \frac{- 2 (1 + t^{2} + 2 t - 2)}{2} ∴ h - (1 + t)^{2} = - 1 - t^{2} - 2 t + 2 \Rightarrow= 2 (1 - t) k = - (t^{2} - 1) ∴ \frac{k}{h} = \frac{- (t - 1) (t + 1)}{2 (1 - t)} \Rightarrow (t + 1) = \frac{2 k}{h} \Rightarrow t = \frac{2 k}{h} - 1 a n d 1 - t = 2 - \frac{2 k}{h} = \frac{h}{2} ∴ 2 h - 2 k = \frac{h^{2}}{2} \Rightarrow 4 x - 4 y = x^{2} ∴ A + B = 0$

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