How do you graph X^2+Y^2-10X-4Y+28=0?

Jun 6, 2016

A circle with centre $\left(5 , 2\right)$ and a radius of $1$ unit.

Explanation:

Complete the square to identify relevant features in this graph.

${X}^{2} + {Y}^{2} - 10 X - 4 Y + 28 = 0$
${X}^{2} - 2 \left(5\right) X + {5}^{2} + {Y}^{2} - 2 \left(2\right) Y + {2}^{2} = {5}^{2} + {2}^{2} - 28$
${\left(X - 5\right)}^{2} + {\left(Y - 2\right)}^{2} = 1$

Thus, we see that this graph is a circle with centre $\left(5 , 2\right)$ and a radius of $1$ unit.