JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P\) be a point on the parabola, \(y^{2}=12 x\) and \(N\) be the foot of the perpendicular drawn from \(P\) on the axis of the parabola. A line is now drawn through the mid-point \(M\) of \(PN\), parallel to its axis which meets the parabola at \(Q\). If the \(y\)-intercept of the line \(NQ\) is \(\frac{4}{3},\) then
- A \(MQ =\frac{1}{3}\)
- B \(PN =3\)
- C \(MQ =\frac{1}{4}\)
- D \(PN =4\)
Answer & Solution
Correct Answer
(C) \(MQ =\frac{1}{4}\)
Step-by-step Solution
Detailed explanation
Let \(P =\left(3 t ^{2}, 6 t \right) ; N =\left(3 t ^{2}, 0\right)\) \(M =\left(3 t ^{2}, 3 t \right)\) Equation of \(MQ : y =3 t\) \(\therefore \quad Q=\left(\frac{3}{4} t^{2}, 3 t\right)\) Equation of NQ…
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