Question

If a circle is centered at (5,-7) and goes through the point (-3,-1) what is the radius

Answer 1

well, we know its center and a point on it, and the distance from its center to a point is its radius

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{ center }{(\stackrel{x_1}{5}~,~\stackrel{y_1}{-7})}\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{ radius }{r}=√((~~-3 - 5~~)^2 + (~~1 - (-7)~~)^2) \implies r=√((-3 -5)^2 + (1 +7)^2) \\\\\\ r=√(( -8 )^2 + ( 8 )^2) \implies r=√( 64 + 64 ) \implies r=√( 128 )\implies r\approx 11.31`