JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let O be the vertex of the parabola \(y^2=4x\) and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is:
- A \(1\)
- B \(2\)
- C \(4\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Let the vertex of the parabola \(y^2 = 4x\) be \(O(0, 0)\). Let the coordinates of the points \(P\) and \(Q\) on the parabola be \((t_1^2, 2t_1)\) and \((t_2^2, 2t_2)\) respectively. The slope of the chord \(OP\) is \(m_1 = \dfrac{2t_1 - 0}{t_1^2 - 0} = \dfrac{2}{t_1}\). The…
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