Solution - Properties of circles

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

$$d=2\cdot r$$

r=85

$$d=2\cdot 85$$

$$d=170$$

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=85

$$c=2\cdot 85\cdot \pi$$

$$c=170\cdot \pi$$

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

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

r=85

$$a={85}^2\cdot \pi$$

$$a=7225\cdot \pi$$

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:
$$c^2+d^2=7225$$
$$h=0$$
$$k=0$$
Center $$\left(0,0\right)$$

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 $$x$$:

$${\left(c+0\right)}^2+{\left(d+0\right)}^2=7225$$

$${\left(c+0\right)}^2+{\left(0+0\right)}^2=7225$$

$${\left(c+0\right)}^2+{\left(-0\right)}^2=7225$$

$${\left(c+0\right)}^2+0=7225$$

$${\left(c+0\right)}^2=7225-0$$

$${\left(c+0\right)}^2=7225$$

$$\sqrt{\left({\left(c+0\right)}^2\right)}=\sqrt{\left(7225\right)}$$

$$c+0=\sqrt{\left(7225\right)}$$

$$c=\pm \sqrt{\left(7225\right)}-0$$

$$c=\pm 85-0$$

$$c_1=\left(-85,0\right),c_2=\left(85,0\right)$$

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 $$y$$:

$${\left(c+0\right)}^2+{\left(d+0\right)}^2=7225$$

$${\left(0+0\right)}^2+{\left(d+0\right)}^2=7225$$

$${\left(-0\right)}^2+{\left(d+0\right)}^2=7225$$

$$0+{\left(d+0\right)}^2=7225$$

$${\left(d+0\right)}^2=7225-0$$

$${\left(d+0\right)}^2=7225$$

$$\sqrt{\left({\left(d+0\right)}^2\right)}=\sqrt{\left(7225\right)}$$

$$d+0=\sqrt{\left(7225\right)}$$

$$d=\pm \sqrt{\left(7225\right)}-0$$

$$d=\pm 85-0$$

$$d_1=\left(0,-85\right),d_2=\left(0,85\right)$$