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AP EAMCET202119 Aug 2021Evening ShiftMathematicsParabolaActual

Find the equation of the parabola which passes through ( 6 , - 2 ) , has its vertex at the origin and its axis along the y - axis.

Options

  1. Ay 2 = 18 x
  2. Bx 2 = 18 y
  3. Cy 2 = − 18 x
  4. Dx 2 = − 18 y

Correct answer

D. x 2 = − 18 y

Step-by-step solution

As given, the vertex of the parabola is origin and it's axis is along the y - axis, So, the standard equation of the parabola with given conditions is, x 2 = - 4 a y     . . . 1 , as it passes through 6 ,   - 2 Hence, x 2 = - 4 a y   ⇒   6 2 = - 4 × a × - 2   ⇒   a = 36 8 = 9 2 So, substituting the value of a in equation 1 The equation is x 2 = - 18 y

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