Question

The center of a circle is (3, -1). One point on the circle is (6,2). Find the equation of the circle

Answer 1

the distance from the center of a circle to a point on the circle goes by the name of radius, so the distance between these two points is just that.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{radius}{r}=√([6-3]^2+[2-(-1)]^2)\implies r=√((6-3)^2+(2+1)^2) \\\\\\ r=√(3^2+3^2)\implies r=√(18) \\\\[-0.35em] ~\dotfill`

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{√(18)}{ r}\\[2em] [x-3]^2+[y-(-1)]^2=(√(18))^2\implies (x-3)^2+(y+1)^2=18`