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2.3 - 2014 Q9

Picture
Figure 3 shows a circle C with centre Q and radius 4 and the point T which lies on C.
The tangent to C at the point T passes through the origin O and OT = 6√5
Given that the coordinates of Q are (11, k), where k is a positive constant,

(a) find the exact value of k, (3)

(b) find an equation for C. (2)
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