By definition, the standard equation of the circle is given by:
[tex](x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2
[/tex]
Where,
(xo, yo): coordinates of the center of the circle
r: radius of the circle
To find the radius of the circle, we use the formula of distance between points.
We have then:
[tex]r=\sqrt{(x2-x1)^2+(y2-y1)^2} [/tex]
Substituting values:
[tex]r=\sqrt{(-2-(-2))^2+(6-10)^2} [/tex]
[tex]r=\sqrt{(-2+2)^2+(-4)^2} [/tex]
[tex]r=\sqrt{(0)^2+16} [/tex]
[tex]r=\sqrt{(0+16} [/tex]
[tex]r=\sqrt{(16} [/tex]
[tex]r=4[/tex]
Then, the center of the circle is:
[tex](xo, yo) = (-2, 6)
[/tex]
Substituting values in the general equation we have:
[tex](x-(-2))^2+(y-6)^2=4^2[/tex]
Rewriting:
[tex](x+2)^2+(y-6)^2=16[/tex]
Answer:
The standard equation of the circle is:
[tex](x+2)^2+(y-6)^2=16[/tex]
