Solve the equation : $x^{2} + y^{2} - 14 x - 6 y - 6 = 0$

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Solution

$\begin{matrix} x^{2} + y^{2} - 14 x - 6 y - 6 = 0 {(x - 7)}^{2} + {(y - 3)}^{2} - 6 = 49 + 9 {(x - 7)}^{2} + {(y - 3)}^{2} = 64 {(x - 7)}^{2} + {(y - 3)}^{2} = 8^{2} S o, x - 7 = 8 cos θ y - 3 = 8 sin θ x = 8 cos θ + 7, y = (8 sin θ + 3) 3 x + 4 y = 3 (8 cos θ + 7) + 4 (8 sin θ + 3) = 24 cos θ + 21 + 32 sin θ + 12 = 24 cos θ + 32 sin θ + 33 \sqrt{24^{2} + 32^{2} + 33} = 40 + 33 = 73 \end{matrix}$

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