Question 104936
Find the standard form of the equation of the circle which passes through the point (4, -5) and center at (-2,3)
The standard form of a circle centered at (h,k) is
{{{(x-h)^2+(y-k)^2=R^2}}}
We can calculate R using the center and the point provided. 
The distance between the two points equals the radius. 
{{{D^2=R^2=(x[2]-x[1])^2+(y[2]-y[1])^2}}} Distance = Radius
{{{(x-(-2))^2+(y-3)^2=(4-(-2))^2+(-5-3)^2}}} PLug in all the values
{{{(x+2)^2+(y-3)^2=(6)^2+(-8)^2}}} Simplify. 
{{{(x+2)^2+(y-3)^2=100}}} Final answer.
Circle with center (-2,3) and passing through (4,-5) has a radius of 10.