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QJEEAdv23Maf8bf: JEE Advanced 2023 Mathematics - Class 11 JEEAdv23Maf8bf Solution: Let be a point on the parabola , where . The normal to the…

Let PP be a point on the parabola y2=4axy^2=4 a x , where a>0 . The normal to the parabola at PP meets the xx -axis at a point QQ . The area of the triangle PFQP F Q , where FF is the focus of the parabola, is 120 . If the slope mm of the normal and aa are both positive integers, then the pair (a,m)(a, m) is

Multiple Choice Options

  • A (2,3)(2,3)
  • B (1,3)(1,3)
  • C (2,4)(2,4)
  • D (3,4)(3,4)

Step-by-Step Verified Solution

JEE Advanced 2023 Paper 1 Online Mathematics - Parabola Question 3 English Explanation

y2=4ax

Equation of normal

y=mx−2am−am3

Point of contact

P(am2,−2am)

and Point Q(2a+am2,0)Q\left(2 a+a m^2, 0\right)

Area of

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Satisfies the equation (1)(1) , hence (2,3)(2,3) will be the correct answer.

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