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JEE Main202224 Jun 2022Evening ShiftMathematicsParabolaActual

A particle is moving in the x y -plane along a curve C passing through the point 3 , 3 . The tangent to the curve C at the point P meets the x -axis at Q . If the y -axis bisects the segment P Q , then C is a parabola with

Options

  1. Alength of latus rectum 3
  2. Blength of latus rectum 6
  3. Cfocus 4 3 , 0
  4. Dfocus 0 , 3 3

Correct answer

A. length of latus rectum 3

Step-by-step solution

Let Point P x , y So equation of line passing through P x , y will be Y - y = m X - x Point on x -axis is given by Q x - y m , 0 Mid-point of P Q lies on y axis so its x co-ordinate will be zero, x - y m + x = 0 m = y 2 · x ⇒ 2 d y y = d x x 2 lnn = ln x + ln k y 2 = k x It passes through 3 , 3 ⇒ k = 3 curve c ⇒ y 2 = 3 x Length of L.R. = 3 Focus = 3 4 , 0

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