3.30: Tangent line to a curve from a linear condition

0606/21/M/J/23 — Question 11 · 9 marks

The line x+3y=kx + 3y = k, where kk is a positive constant, is a tangent to the curve x2+y2+2y9=0x^{2} + y^{2} + 2y - 9 = 0. Find the value of kk and the coordinates of the point of contact.
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