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AP EAMCET202120 Aug 2021Morning ShiftMathematicsParabolaActual

The coordinates of the focus of the parabola described parametrically by x = 5 t 2 + 2 , y = 10 t + 4 (where t is a parameter) are

Options

  1. A( 7 , 4 )
  2. B( 3 , 4 )
  3. C( 3 , - 4 )
  4. D( - 7 , 4 )

Correct answer

A. ( 7 , 4 )

Step-by-step solution

Given parametric curves are x = 5 t 2 + 2 ,   y = 10 t + 4 ⇒ x - 2 5 = t 2 , y - 4 10 = t Eliminating t , we get x - 2 5 = y - 4 10 2 ⇒ y - 4 2 = 20 x - 2 ⇒ Y 2 = 10 X , where Y = y - 4 ,   X = x - 2 Coordinates of focus are 5 , 0 So, x - 2 = 5 ,   y - 4 = 0 ⇒ x = 7 ,   y = 4 Hence, required coordinates are 7 , 4

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