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Question

AB is a chord of the parabola y2=4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. the projection of BC on the x-axis is ka. What's the value of 'k'?


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Solution

Here we are asked to find the projection of BC on the x-axis.

This is equal to the difference in the x coordinates of points B and C.

LetB(at2,2at)

Lets first get the equation of BC

Slope of AB=2at0at20=2t

Equation of BC is,

y2at=(t2)(xat2)

for getting point C. solve BC with x-axis

2at=[t2].(xat2)

4a=xat2

x=4a+at2

C(4a+at2,0)

projection of BC on x-axis is =4a+at2at2

                                                                      ka=4a

                                                   k=4

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