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:

$$c=2r\pi$$
$$r=5$$
$$c=2·5\pi$$
$$c=10\pi$$

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

$$a=r^2\pi$$
$$r=5$$
$$a=5^2\pi$$
$$a=25\pi$$

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:

$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
$$h=-5$$
$$k=4$$
$$r=5$$
$${\left(x+5\right)}^2+{\left(y-4\right)}^2=5^2$$
$${\left(x+5\right)}^2+{\left(y-4\right)}^2=25$$

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: