# How do you find the equation of the circle with centre at (4,-1) and passing through (0,2)?

Feb 13, 2016

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

#### Explanation:

Here is the recipe for solving this type of problem:
1) Determine Radius: Find the distance between the point on the circle and center, that is the radius
2) Write the general circle equation form: ${\left(x - h\right)}^{2} + {\left(y - k\right)}^{2} = {r}^{2}$ where (h, k) is the center of the cicle

Step1 Radius - Use distance formula:
${r}^{2} = {\left({x}_{1} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}$
${r}^{2} = {\left(4 - 0\right)}^{2} + {\left(- 1 - 2\right)}^{2} = 25$

Step2 Radius - Use distance formula:
${\left(x - 4\right)}^{2} + {\left(y + 1\right)}^{2} = {5}^{2}$