Write the parametric equations of the circle $2 x^{2} + 2 y^{2} - 5 x - 7 y - 3 = 0$

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Solution

$2 x^{2} + 2 y^{2} - 5 x - 7 y - 3 = 0$
$x^{2} + y^{2} - \frac{5}{2} x - \frac{7}{2} y = \frac{3}{2}$
$x^{2} - \frac{5}{2} x + \frac{25}{16} + y^{2} - \frac{7}{2} y + \frac{49}{16} = \frac{3}{2} + \frac{25}{16} + \frac{49}{16}$
$(x - 5 / 4)^{2} + (y - 7 / 4)^{2} = \frac{3}{2} + \frac{74}{16} = \frac{98}{16} = \frac{48}{8}$
$x - 5 / 4 = \frac{7}{2 \sqrt{2}} cos θ$ $y - 7 / 4 = \frac{7}{2 \sqrt{2}} sec θ$
$x = \frac{5}{4} + \frac{7}{2 \sqrt{2}} cos θ$ $y = \frac{7}{4} + \frac{7}{2 \sqrt{2}} sin θ$

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