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AP EAMCET202418 May 2024Morning ShiftMathematicsParabolaActual

The line x-2 y-3=0 cuts the parabola y^2=4 ax at the points P and Q . If the focus of this parabola is ( 1 4 , k ) , then P Q=

Options

  1. A16 a 5
  2. B8 a 5
  3. C4 a 5
  4. D2 a 5

Correct answer

A. 16 a 5

Step-by-step solution

Given the equation of the parabola y^2=4 a x and focus of this parabola is ( 1 4 , k ) . (a, 0)= ( 1 4 , k ) k=0, a= 1 4 Since, x-2 y-3=0 x=2 y+3 Now, y^2=4 1 4 x y^2=2 y+3 aligned & y^2-2 y+3=0 (y-3)(y+1)=0 & y=-1,3 x=1,9 aligned Let P (1,-1) and Q (9,3) aligned & P Q= 8^2+4^2 = 80 =4 5 & =4 4 1 4 5 =16 a 5 aligned

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