JEE Advanced 2023 Mathematics question

MathematicsApplication of DerivativesJEE Advanced 2023

Let be a point on the parabola , where . The normal to the parabola at meets the -axis at a point . The area of the triangle , where is the focus of the parabola, is 120. If the slope of the normal and are both positive integers, then the pair is

Answer: (A)

Solution

; the normal has slope and equation , meeting the -axis at . With : and the height is

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Question ID VK-034068