Solution - Properties of circles from center point and radius/diameter

A circle's circumference ($$c$$) equals twice the length of its radius ($$r$$) times π. To find the circumference plug r into the formula:

$$c=2r\pi$$
$$r=2.5$$
$$c=2·2.5\pi$$
$$c=5\pi$$

A circle's area ($$a$$) equals its radius ($$r$$) squared times π. To find the area, plug $$r$$ into the formula:

$$a=r^2\pi$$
$$r=2.5$$
$$a={2.5}^2\pi$$
$$a=6.25\pi$$

The standard form of the equation of a circle is $${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$, in which $$h$$ represents the x-coordinate of the circle's center, $$k$$ represents the y-coordinate of the circle's center, $$r$$ represents the circle's radius, and $$x$$ and $$y$$ represent the coordinates of any point on the circle's perimeter.
To find the equation of the circle in standard form, plug $$h,k$$ and $$r$$ into the equation:

$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
$$h=-8$$
$$k=0$$
$$r=2.5$$
$${\left(x+8\right)}^2+y^2={2.5}^2$$
$${\left(x+8\right)}^2+y^2=6.25$$

The expanded form of the equation of a circle is $$x^2+y^2+ax+by+c=0$$. To find the equation of the circle in expanded form, expand the standard form of the equation of a circle: