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AP EAMCET2006MathematicsParabola

Let O be the origin and A be a point on the curve y^2=4 x . Then the locus of the mid point of O A is :

Options

  1. Ax^2=4 y
  2. Bx^2=2 y
  3. Cy^2=16 x
  4. Dy^2=2 x

Correct answer

D. y^2=2 x

Step-by-step solution

Since O be the origin and A be the point on the curve y^2=4 x . Co-ordinates of O and A are (0,0) and (a t^2, 2 a t ) respectively. Co-ordinates of mid point of O A are ( 0+a t^2 2 , 0+2 a t 2 )= ( a t^2 2 , a t ) (a t)^2=2 ( a t^2 2 ) Thus the locus of required point is y^2=2 x

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