Question

Center: (-9, -3), point on circle: (-11, 2) what is the standard equation for this?

Answer 1

well, what's its radius anyway? wait a second!! the distance from the center to a point on the circle is the radius.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-9}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{-11}~,~\stackrel{y_2}{2})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ r=√((~~-11 - (-9)~~)^2 + (~~2 - (-3)~~)^2) \implies r=√((-11 +9)^2 + (2 +3)^2) \\\\\\ r=√(( -2 )^2 + ( 5 )^2) \implies r=√( 4 + 25 ) \implies r=√( 29 ) \\\\[-0.35em] ~\dotfill`

`\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-9}{h}~~,~~\underset{-3}{k})}\qquad \stackrel{radius}{\underset{√(29)}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-9) ~~ )^2 ~~ + ~~ ( ~~ y-(-3) ~~ )^2~~ = ~~√(29^2)\implies (x+9)^2 + (y+3)^2 = 29`