Ok so the general form of a circle is given by;
(x-a)²+(y-b)²=r²
where a and b are the coordinates of the center
and r is the radius of the circle
For this case we know that the center is (5,-7)
So the general equation of the circle would be;
[tex](x - 5) {}^{2} + (y - ( - 7)) {}^{2} = r {}^{2} [/tex]
[tex](x - 5 {}^{2} + (y + 7) {}^{2} = r {}^{2} [/tex]
Since we know that (-3,-1) is a point on that circle, we can say that it satisfies the equation of the circle;
[tex]( - 3 - 5) {}^{2} + ( - 1 + 7) {}^{2} = r {}^{2} [/tex]
[tex]r {}^{2} = ( - 8) {}^{2} + ( 6) {}^{2} [/tex]
[tex]r {}^{2} = 64 + 36 = 100[/tex]
So now,
[tex](x - 5) {}^{2} + ( {y + 7)}^{2} = 100[/tex]
