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Q.

Let P be a point on the parabola, y2=12xand 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 is43 , then :

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a

MQ=14

b

PN = 3

c

PN = 4

d

MQ=13

answer is A.

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Detailed Solution

M=3t2,3tMQ line is y=3t Solving y2=12x,y=3t⇒x=3t24Q=3t24,3t,N=3t2,0 Equation of NQ is 4x+3ty=12t2x=0⇒y=4t=43( given )⇒t=13MQ=14

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Let P be a point on the parabola, y2=12xand 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 is43 , then :