Solution - Properties of circles

The diameter $$\left(d\right)$$ is equal to twice the radius:
$$d=2·r$$

$$d=2\cdot r$$

r=8.485

$$d=2\cdot 8.485$$

$$d=16.971$$

The circumference $$\left(c\right)$$ is equal to two times the radius times π:
$$c=2·r·\pi$$

$$c=2\cdot r\cdot \pi$$

r=8.485

$$c=2\cdot 8.485\cdot \pi$$

$$c=16.971\cdot \pi$$

The area $$\left(a\right)$$ is equal to the radius squared times π:
$$a=r^2·\pi$$

$$a=r^2\cdot \pi$$

r=8.485

$$a={8.485}^2\cdot \pi$$

$$a=72\cdot \pi$$

The coordinates of the center of a circle are usually, but not always, represented by $$h$$ and $$k$$ in a circle's standard form equation:
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
Identify the $$h$$ and $$k$$ in the equation:
$${\left(x+4\right)}^2+{\left(y-9\right)}^2=72$$
$$h=-4$$
$$k=9$$
Center $$\left(-4,9\right)$$

To find the $$x$$ -intercept(s), substitute $$0$$ for $$y$$ in the circle's standard form equation
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
and solve the quadratic equation for $$x$$:

$${\left(x+4\right)}^2+{\left(y-9\right)}^2=72$$

$${\left(x+4\right)}^2+{\left(0-9\right)}^2=72$$

$${\left(x+4\right)}^2+{\left(-9\right)}^2=72$$

$${\left(x+4\right)}^2+81=72$$

$${\left(x+4\right)}^2=72-81$$

$${\left(x+4\right)}^2=-9$$

$$\sqrt{\left({\left(x+4\right)}^2\right)}=\sqrt{\left(-9\right)}$$

$$x+4=\sqrt{\left(-9\right)}$$

$$x=\pm \sqrt{\left(-9\right)}-4$$

No x-intercepts

To find the $$y$$ -intercept(s), substitute $$0$$ for $$x$$ in the circle's standard form equation
$${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$$
and solve the quadratic equation for $$y$$:

$${\left(x+4\right)}^2+{\left(y-9\right)}^2=72$$

$${\left(0+4\right)}^2+{\left(y-9\right)}^2=72$$

$${\left(4\right)}^2+{\left(y-9\right)}^2=72$$

$$16+{\left(y-9\right)}^2=72$$

$${\left(y-9\right)}^2=72-16$$

$${\left(y-9\right)}^2=56$$

$$\sqrt{\left({\left(y-9\right)}^2\right)}=\sqrt{\left(56\right)}$$

$$y-9=\sqrt{\left(56\right)}$$

$$y=\pm \sqrt{\left(56\right)}+9$$

$$y_1=\left(0,\sqrt{\left(56\right)}+9\right),y_2=\left(0,-\sqrt{\left(56\right)}+9\right)$$