Question

Given the point on a circle at (1,-7) and a center at (-6,-4), write the equation of the circle

Answer 1

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-7})\qquad \stackrel{center}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{radius}{r}=√([-6-1]^2+[-4-(-7)]^2)\implies r=√((-6-1)^2+(-4+7)^2) \\\\\\ r=√((-7)^2+3^2)\implies r=√(58) \\\\[-0.35em] ~\dotfill`

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-6}{ h},\stackrel{-4}{ k})\qquad \qquad radius=\stackrel{√(58)}{ r}\\[2em] [x-(-6)]^2+[y-(-4)]^2=(√(58))^2\implies (x+6)^2+(y+4)^2=56`