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AP EAMCET202423 May 2024Morning ShiftMathematicsParabolaActual

If P is a point which divides the line segment joining the focus of the parabola y^2=12 x and a point on the parabola in the ratio 1:2. Then the locus of P is

Options

  1. Ay^2=2(x-2)
  2. By^2=4 x
  3. Cy^2=4(x-2)
  4. Dy^2=9(x-3)

Correct answer

C. y^2=4(x-2)

Step-by-step solution

Parabola : y^2=12 x Focus =(3,0) Let Q (3 t^2, 6 t ) be a point on the parabola. aligned & P(x, y)= ( 3 t^2+6 3 , 6 t 3 )= (t^2+2,2 t ) & x=t^2+2, y=2 t t= y 2 & x= y^2 4 +2 y^2=4(x-2) aligned

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