Question

Let P be a point on the parabola, y² = 12x 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 4 / 3 , then : 

(1) MQ = 1 / 3 

(2) PN = 3 

(3) MQ = 1 / 4 

(4) PN = 4

Answer 1

(3) MQ = 1 / 4 

y-intercept of NQ = 4t = 4/3 ⇒ t = 1/3

\(\therefore\) MQ = 9/4t² = 1/4

PN = 6t = 2