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COMEDK2013MathematicsParabola

If (0,6) and (0,3) are respectively the vertex and focus of a parabola, then its equation is

Options

  1. Ax²+12 y=72
  2. Bx²-12 y=72
  3. Cy²-12 x=72
  4. Dy²+12 x=72

Correct answer

A. x²+12 y=72

Step-by-step solution

The vertex and focus of the parabola are (0,6) and (0,3) respectively. Clearly, axis is Y -axis. Latusrectum =4 (Distance between vertex and focus) =4 (0-0)²+(6-3)² =12 Also, the vertex is on the right hand side of the focus, so the parabola opens downward. Hence, equation of the parabola is aligned (x-0)² &=-12(y-6) x² &=-12 y+72 & x²+12 y &=72 aligned

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