Find the parametric equation of the circle 2x^2 + 2y ^2 = 5x + 7y +3

Dear Student,

Equation of circle: 2x² + 2y² - 5x - 7y - 3 = 0

x² + y² - $\frac{5}{2}$x - $\frac{7}{2}$y - $\frac{3}{2}$ = 0
x² - 2 $\frac{5}{4}$x + ${\left(\frac{\sqrt{5}}{2}\right)}^2$ + y² - 2 $\frac{7}{4}$y + ${\left(\frac{\sqrt{7}}{2}\right)}^2$ - $\frac{3}{2}$ - ${\left(\frac{\sqrt{5}}{2}\right)}^2$-${\left(\frac{\sqrt{7}}{2}\right)}^2$ = 0
${\left(x-\frac{\sqrt{5}}{2}\right)}^2 + {\left(y-\frac{\sqrt{7}}{2}\right)}^2$ - $\frac{3}{2}$ - $\frac{5}{4}$ - $\frac{7}{4}$ = 0
${\left(x-\frac{\sqrt{5}}{2}\right)}^2 + {\left(y-\frac{\sqrt{7}}{2}\right)}^2$ = $\frac{9}{2}$
${\left(x-\frac{\sqrt{5}}{2}\right)}^2 + {\left(y-\frac{\sqrt{7}}{2}\right)}^2$ = ${\left(\frac{3}{\sqrt{2}}\right)}^2$
Hence, the parametric equation of the circle is: 

x = $\frac{\sqrt{5}}{2}+\frac{3}{\sqrt{2}}\cos \theta$ and y = $\frac{\sqrt{7}}{2}+\frac{3}{\sqrt{2}}\sin \theta$

Regards