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1 Pure Mathematics

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Question 106

The curve C C\,C has parametric equations

x=2tx = 2tx=2t, y=t2−ky = t^2 - ky=t2−k

where k k\,k is a positive constant.

C C\,C meets the line y=xy = xy=x at two points, A A\,A and BBB.

a.

Show that the xxx-coordinates of A A\,A and B B\,B satisfy

x2−4x−4k=0x^2 - 4x - 4k = 0x2−4x−4k=0

[3]
b.

Given that the length of AB AB\,AB is 50\sqrt{50}50​, find the value of kkk.

[5]
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1 Pure Mathematics Questions

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