Answer:
The equation of the circle is [tex](x + 4)^2 + (y - 10)^2 = 64[/tex], third option is correct.
Step-by-step explanation:
Equation of a circle:
The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Center at (-4, 10)
This means that [tex]x_0 = -4, y_0 = 10[/tex].
Radius of 8:
This means that [tex]r = 8[/tex]. So
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - (-4))^2 + (y - 10)^2 = 8^2[/tex]
[tex](x + 4)^2 + (y - 10)^2 = 64[/tex]
The equation of the circle is [tex](x + 4)^2 + (y - 10)^2 = 64[/tex], third option is correct.
