JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(PQ\) be a double ordinate of the parabola, \(y^2\, = - 4x\), where \(P\) lies in the second quadrant. If \(R\) divides \(PQ\) in the ratio \(2 : 1\) then the locus of \(R\) is
- A \(3y^2\, = - 2x\)
- B \(3y^2\, = 2x\)
- C \(9y^2\, = 4x\)
- D \(9y^2\, = - 4x\)
Answer & Solution
Correct Answer
(D) \(9y^2\, = - 4x\)
Step-by-step Solution
Detailed explanation
Let \(P\left( { - at_1^2,2a{t_1}} \right),Q\left( { - at_1^2, - 2a{t_1}} \right)\) and \(R(h,k)\) By using section formula, we have \(h = - at_1^2,k = \frac{{ - 2a{t_1}}}{3}\) \(k = - \frac{{2a{t_1}}}{3}\) \( \Rightarrow 3k = - 2a{t_1}\)…
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