# How do you find the equation for the circle centered at (0,0) that passes through the point (1,-6)?

Sep 29, 2016

${x}^{2} + {y}^{2} = 37$

#### Explanation:

The equation of a circle of center(a,b) and radius r is :
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

So,to think about the equation of a circle we should think about its center and radius .

The center is given (0,0).
The circle passes through the point (1,-6) so ,
the radius is the distance between (0,0) and (1,-6)

${r}^{2} = {\left(1 - 0\right)}^{2} + {\left(- 6 - 0\right)}^{2}$
${r}^{2} = 1 + 36 = 37$

Equation of a circle is:

${\left(x - 0\right)}^{2} + {\left(y - 0\right)}^{2} = 37$
${x}^{2} + {y}^{2} = 37$