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1 Pure Mathematics

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Question 302

The circle C C\,C has equation x2+y2+8x−4y+k=0x^2 + y^2 + 8x - 4y + k = 0x2+y2+8x−4y+k=0 where k k\,k is a constant.

C C\,C passes through the point (1,5)(1, 5)(1,5).

a.

Find the value of kkk.

[2]
b.

Use completing the square to identify the centre of C C\,C and its exact radius.

[3]
c.

A straight line that passes through the point A(3,7)A(3, 7)A(3,7) is a tangent to C C\,C at the point BBB. Find the exact length ABABAB.

[4]
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1 Pure Mathematics Questions

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