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  • Let P be a point on the parabola,  and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through mid-po

Let P be a point on the parabola, y^{2}=12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through mid-point M of PN, parallel to its axis which meets the parabola at Q. If the y-intercept of the NQ is \frac{4}{3}, then:
Option: 1 PN=4
Option: 2 MQ=\frac{1}{3}
Option: 3 MQ=\frac{1}{4}  
Option: 4 PN=3

Answers (1)

best_answer

P=(3t^{2},6t), N =(3t^{2},0)

M=(3t^{2},3t), Q =\left (\frac{3}{4}t^{2},3t \right )

\therefore t=\frac{1}{3}\

\\\therefore \mathrm{MQ}=\frac{9}{4} \mathrm{t}^{2}=\frac{1}{4} \text{ and } \mathrm{PN}=6 \mathrm{t}=2

Posted by

Suraj Bhandari

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