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Let P be the point (1,0) and Q a point on the locus y^2=8 x . The locus of mid point of P Q is

Options

  1. Ay^2-4 x+2=0
  2. By^2+4 x+2=0
  3. Cx^2+4 y+2=0
  4. Dx^2-4 y+2=0

Correct answer

A. y^2-4 x+2=0

Step-by-step solution

P =(1,0)Q=(h, k) such that k^2=8 h Let ( , ) be the midpoint of PQ aligned & = h +1 2 , = k +0 2 & 2 -1= h , 2 = k . & (2 )^2=8(2 -1) ^2=4 -2 & y ^2-4 x +2=0 . aligned

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