Answer:
[tex]\large\boxed{A.\ (x+6)^2+(y+10)^2=20}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the endpoints of the diameter of a circle (-8, -6) and (-4, -14).
The midpoint of a diameter is a center of a circle.
The formula of a midpoint:
[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
Substitute:
[tex]x=\dfrac{-8+(-4)}{2}=\dfrac{-12}{2}=-6\\\\y=\dfrac{-6+(-14)}{2}=\dfrac{-20}{2}=-10[/tex]
We have h = -6 and k = -10.
The radius is the distance between a center and the point on a circumference of a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute (-6, -10) and (-8, -6):
[tex]r=\sqrt{(-8-(-6))^2+(-6-(-10))^2}=\sqrt{(-2)^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]
Finally we have
[tex](x-(-6))^2+(y-(-10))^2=(\sqrt{20})^2\\\\(x+6)^2+(y+10)^2=20[/tex]
Answer:
It's A...Just had it but i Chose B but it's A
Step-by-step explanation:
