# What is the standard form of the equation of a circle with centre (1,7) passing through the point (-4,-5)?

Nov 13, 2015

${\left(x - 1\right)}^{2} + {\left(y - 7\right)}^{2} = 169$

#### Explanation:

The distance from the point (1,7) to the point (-4,-5) is
$\sqrt{{\left(- 4 - 1\right)}^{2} + {\left(- 5 - 7\right)}^{2}} = 13$.

Thus the radius of the circle is 13.

But the general form of a circle centred at (a,b) and having radius r is given by
${\left(x - a\right)}^{2} + {\left(y - b\right)}^{2} = {r}^{2}$

Therefore the equation for this particular circle is

${\left(x - 1\right)}^{2} + {\left(y - 7\right)}^{2} = 169$