Answer:
Option C [tex](x-1)^2+(y+1)^2=80[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The distance from the center of the circle to any point on the circumference of the circle is equal to the radius of the circle
we have
(1,-1) and (5,7)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
substitute the values
[tex]d=\sqrt{(7+1)^{2}+(5-1)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{80}\ units[/tex]
step 2
Find the equation of the circle in center radius form
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where
(h,k) is the center
r is the radius
substitute
[tex](x-1)^2+(y+1)^2=(\sqrt{80})^2[/tex]
[tex](x-1)^2+(y+1)^2=80[/tex]
