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The coordinates of the focus of the parabola described parametrically by x = 5 t 2 + 2 ,   y = 10 t + 4 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 or x - 2 5 = t 2 ,   y - 4 10 = t ⇒   x - 2 5 =   y - 4 10 2 ⇒   y - 4 2 = 20 x - 2 ⇒   Y 2 = 20 X ,   w h e r e   Y = y - 4 ,   X = x - 2 ∴ Coodinate of focus is ( 5 ,   0 ) i e , x - 2 = 5 ,   y - 4 = 0 ⇒     x = 7 ,   y = 4 Hence, the required coordinate is ( 7 ,   4 )

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