JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let chord PQ of length \(3\sqrt{13}\) of the parabola \(y^2 = 12x\) be such that the ordinates of points \(P\) and \(Q\) are in the ratio \(1:2\). If the chord PQ subtends an angle \(\alpha\) at the focus of the parabola, then \(\sin\alpha\) is equal to:
- A \(\dfrac{3}{5}\)
- B \(\dfrac{4}{5}\)
- C \(\dfrac{5}{13}\)
- D \(\dfrac{12}{13}\)
Answer & Solution
Correct Answer
(A) \(\dfrac{3}{5}\)
Step-by-step Solution
Detailed explanation
Let the coordinates of points \(P\) and \(Q\) on the parabola \(y^2 = 12x\) be \((x_1, y_1)\) and \((x_2, y_2)\). Given that the ordinates are in the ratio \(1:2\), we have \(y_2 = 2y_1\). Since \(P\) and \(Q\) lie on the parabola, their abscissae are \(x_1 = \dfrac{y_1^2}{12}\)…
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