Question

What is the equation of a circle that has a center at (-4, 10) and a radius of 8?

Answer 1

Answer:

The equation of the circle is $(x + 4)^2 + (y - 10)^2 = 64$, third option is correct.

Step-by-step explanation:

Equation of a circle:

The equation of a circle with center $(x_0,y_0)$ and radius r is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

Center at (-4, 10)

This means that $x_0 = -4, y_0 = 10$.

Radius of 8:

This means that $r = 8$. So

$(x - x_0)^2 + (y - y_0)^2 = r^2$

$(x - (-4))^2 + (y - 10)^2 = 8^2$

$(x + 4)^2 + (y - 10)^2 = 64$

The equation of the circle is $(x + 4)^2 + (y - 10)^2 = 64$, third option is correct.