# How do you write the equation for a circle with with Radius 10 and centre (2, 1)?

Apr 27, 2016

${x}^{2} + {y}^{2} - 4 x - 2 y - 95 = 0$

#### Explanation:

As the center is $\left(2 , 1\right)$ and radius $10$, circle is locus of a point that is at a distance $10$ from $\left(2 , 1\right)$.

Hence, ${\left(x - 2\right)}^{2} + {\left(y - 1\right)}^{2} = {10}^{2}$ or

${x}^{2} - 4 x + 4 + {y}^{2} - 2 y + 1 = 100$ or

${x}^{2} + {y}^{2} - 4 x - 2 y + 5 - 100 = 0$ or

${x}^{2} + {y}^{2} - 4 x - 2 y - 95 = 0$