COMEDK · Maths · 13. Parabola
If \((0,6)\) and \((0,3)\) are respectively the vertex and focus of a parabola, then its equation is
- A \(x^{2}+12 y=72\)
- B \(x^{2}-12 y=72\)
- C \(y^{2}-12 x=72\)
- D \(y^{2}+12 x=72\)
Answer & Solution
Correct Answer
(A) \(x^{2}+12 y=72\)
Step-by-step Solution
Detailed explanation
The vertex and focus of the parabola are \((0,6)\) and \((0,3)\) respectively. Clearly, axis is \(Y\)-axis. \(\therefore\) Latusrectum \(=4\) (Distance between vertex and focus) \[ =4 \sqrt{(0-0)^{2}+(6-3)^{2}}=12 \] Also, the vertex is on the right hand side of the focus, so…
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