WBJEE · Maths · Parabola
Let \(O\) be the vertex, \(Q\) be any point on the parabola \(x^2=8 y\). If the point \(P\) divides the line segment \(O Q\) internally in the ratio \(1: 3\), then the locus of \(P\) is
- A \(x^2=y\)
- B \(y^2=x\)
- C \(y^2=2 x\)
- D \(x^2=2 y\)
Answer & Solution
Correct Answer
(D) \(x^2=2 y\)
Step-by-step Solution
Detailed explanation
Hint : \(\begin{aligned} & O P: P Q=1: 3 \\ & \Rightarrow \mathrm{h}=\mathrm{t}, \mathrm{k}=\frac{\mathrm{t}^2}{2} \\ & \Rightarrow \mathrm{k}=\frac{\mathrm{h}^2}{2}\end{aligned}\)
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