JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let the locus of the mid-point of the chord through the origin O of the parabola \( y^{2}=4x \) be the curve S. Let P be any point on S. Then the locus of the point, which internally divides OP in the ratio 3:1, is:
- A \(3 y^2=2 x\)
- B \(2 y^2=3 x\)
- C \(3 x^2=2 y\)
- D \(2 x^2=3 y\)
Answer & Solution
Correct Answer
(B) \(2 y^2=3 x\)
Step-by-step Solution
Detailed explanation
\(y^2=4 x\) Locus of mid point of OP \(M ( h , k ) \Rightarrow h =\frac{ t ^2}{2}, k = t\) \(\Rightarrow k^2=2 h \Rightarrow y^2=2 x\) \(S: y^2=2 x\) \(\Rightarrow h =\frac{\frac{3 t ^2}{2}}{4}, k =\frac{3 t }{4}\) \(t ^2=\frac{8 h}{3}, t =\frac{4 k }{3}\)…
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