Draw the circles whose equation are
$5 x^{2} + 5 y^{2} = 2 x + 3 y$ .

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Solution

The given equation of circle is $5 x^{2} + 5 y^{2} = 2 x + 3 y .$

Making perfect square, the equation of circle becomes
${(x - \frac{1}{5})}^{2} + {(y - \frac{3}{10})}^{2} = {(\frac{\sqrt{13}}{10})}^{2}$

Centre is $C (\frac{1}{5}, \frac{3}{10})$ and radius is $r = \frac{\sqrt{13}}{10}$

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