JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The ordinates of the points \(P\) and \(Q\) on the parabola with focus \((3,0)\) and directrix \(x =-3\) are in the ratio \(3: 1\). If \(R (\alpha, \beta)\) is the point of intersection of the tangents to the parabola at \(P\) and \(Q\), then \(\frac{\beta^2}{\alpha}\) is equal to \(.............\).
- A \(16\)
- B \(14\)
- C \(12\)
- D \(10\)
Answer & Solution
Correct Answer
(A) \(16\)
Step-by-step Solution
Detailed explanation
Parabola is \(y^2=12 x\) Let \(Q\left(3 t^2, 6 t\right)\) so \(P \left(27 t ^2, 18 t \right)\) \(R (\alpha, \beta)=\left( at _1 t _2, a \left( t _1+ t _2\right)\right)\) \(=(3 t \cdot 3 t , 3( t +3 t ))\) \(R (\alpha, \beta)=\left(9 t ^2, 12 t \right)\)…
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