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JEE Main20236 Apr 2023Morning ShiftMathematicsApplication of DerivativesActual

Let the tangent to the curve x 2 + 2 x - 4 y + 9 = 0 at the point P 1 , 3 on it meet the y - axis at A . Let the line passing through P and parallel to the line x - 3 y = 6 meet the parabola y 2 = 4 x at B . If B lies on the line 2 x - 3 y = 8 , then A B 2 is equal to _ _ _ _ _ _ _ .

Correct answer

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Step-by-step solution

Given, The tangent to the curve x 2 + 2 x - 4 y + 9 = 0 at the point P 1 , 3 on it meet the y - axis at A , So, tangent to circle at point P 1 , 3 is given by, x + x + 1 - 2 y + 3 + 9 = 0 ⇒ 2 x - 2 y = - 4 So, on y - axis, A 0 , 2 And the line passing through P and parallel to the line x - 3 y = 6 meet the parabola y 2 = 4 x at B , So, the equation of line through P will be y - 3 = 1 3 x - 1 ⇒ 3 y = x + 8 Now finding intersection of y 2 = 4 x   &   3 y = x + 8 we get, B = 4 , 4   &#38

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