# How do you find the center and radius of the circle 2x²+2y²-5x+y=0?

Feb 11, 2017

This is the equation of a circle, center $\left(\frac{5}{4} , - \frac{1}{4}\right)$ and radius $\sqrt{\frac{13}{8}}$

#### Explanation:

Let's rearrange the equation and complete the squares

$2 {x}^{2} - 5 x + 2 {y}^{2} + y = 0$

$2 \left({x}^{2} - \frac{5}{2} x\right) + 2 \left({y}^{2} + \frac{1}{2} y\right) = 0$

$2 \left({x}^{2} - \frac{5}{2} x + \frac{25}{16}\right) + 2 \left({y}^{2} + \frac{1}{2} y + \frac{1}{16}\right) = \frac{25}{8} + \frac{1}{8}$

$2 {\left(x - \frac{5}{4}\right)}^{2} + 2 {\left(y + \frac{1}{4}\right)}^{2} = \frac{26}{8}$

${\left(x - \frac{5}{4}\right)}^{2} + {\left(y + \frac{1}{4}\right)}^{2} = \frac{26}{16} = \frac{13}{8}$

This is the equation of a circle, center $\left(\frac{5}{4} , - \frac{1}{4}\right)$ and radius $\sqrt{\frac{13}{8}}$