Question

Help me finished my work pls!!!!!!

Answer 1

well, yes, its center is at (-1 , 1), now, we have a nice blue point on the IV Quadrant, namely at (6 , -4), so we know the circle passes through (6 , -4), let's check for that distance from the center to that blue point.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{1})}\qquad \stackrel{blue~point}{(\stackrel{x_2}{6}~,~\stackrel{y_2}{-4})}\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√((~~6 - (-1)~~)^2 + (~~-4 - 1~~)^2) \implies d=√((6 +1)^2 + (-4 -1)^2) \\\\\\ d=√(( 7 )^2 + ( -5 )^2) \implies d=√( 49 + 25 ) \implies d=√( 74 ) \\\\[-0.35em] ~\dotfill`

`(x + 1)^2~~ + ~~(y-1)^2~~ = ~~(√(74))^2\implies (x + 1)^2~~ + ~~(y-1)^2~~ = ~~74`