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Let P be the mid-point of a chord joining the vertex of the parabola y²=8 x to another point on it. Then, the locus of P is

Options

  1. Ay²=2 x
  2. By²=4 x
  3. Cx² 4 +y²=1
  4. Dx²+ y² 4 =1

Correct answer

B. y²=4 x

Step-by-step solution

Let the chord be MN. Let other end of chord joining from vertex to it lying on y²=8 x be N (2 t², 4 t ) Mid-point of M N= (t², 2 t ) x=t², y=2 t x= ( y 2 )² y²=4 x is the required locus of P

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