How do you write the standard from of the equation of the circle given Center(4,7) and passing through (3,-2)?

Oct 6, 2016

You need to find the radius first using the center and the point. then remember to use r squared for the radius portion.

Explanation:

${\left(x - 4\right)}^{2} + {\left(y - 7\right)}^{2} = {r}^{2}$

Use the distance formula to find the radius (the pythagorean theorem). I like to draw the picture so it is easier to see the sides of the triangle and make the math easier.

graph{(x-4)^2 + (y-7)^2=sqrt(82) [-40, 40, -20, 20]}

The radius is $r = \sqrt{{\left(3 - 4\right)}^{2} + {\left(- 2 - 7\right)}^{2}}$

$r = \sqrt{{1}^{2} + {9}^{2}} = \sqrt{82}$

So the equation is: ${\left(x - 4\right)}^{2} + {\left(y - 7\right)}^{2} = 82$