Find circle given the center $$$\left(-4, 9\right)$$$, the diameter $$$10$$$

The standard form of the equation of a circle is $$$\left(x - h\right)^{2} + \left(y - k\right)^{2} = r^{2}$$$, where $$$\left(h, k\right)$$$ is the center of the circle and $$$r$$$ is the radius.

Thus, $$$h = -4$$$, $$$k = 9$$$.

Since $$$d = 2 r$$$, then $$$2 r = 10$$$.

Solving the system $$$\begin{cases} h = -4 \\ k = 9 \\ 2 r = 10 \end{cases}$$$, we get that $$$h = -4$$$, $$$k = 9$$$, $$$r = 5$$$ (for steps, see system of equations calculator).

The standard form is $$$\left(x + 4\right)^{2} + \left(y - 9\right)^{2} = 25$$$.

The general form can be found by moving everything to the left side and expanding (if needed): $$$x^{2} + 8 x + y^{2} - 18 y + 72 = 0$$$.

Radius: $$$r = 5$$$.

Area: $$$A = \pi r^{2} = 25 \pi$$$.

Both eccentricity and linear eccentricity of a circle equal $$$0$$$.

The x-intercepts can be found by setting $$$y = 0$$$ in the equation and solving for $$$x$$$ (for steps, see intercepts calculator).

Since there are no real solutions, there are no x-intercepts.

The y-intercepts can be found by setting $$$x = 0$$$ in the equation and solving for $$$y$$$: (for steps, see intercepts calculator).

y-intercepts: $$$\left(0, 6\right)$$$, $$$\left(0, 12\right)$$$

The domain is $$$\left[h - r, h + r\right] = \left[-9, 1\right]$$$.

The range is $$$\left[k - r, k + r\right] = \left[4, 14\right]$$$.

Standard form/equation: $$$\left(x + 4\right)^{2} + \left(y - 9\right)^{2} = 25$$$A.

General form/equation: $$$x^{2} + 8 x + y^{2} - 18 y + 72 = 0$$$A.

Graph: see the graphing calculator.

Center: $$$\left(-4, 9\right)$$$A.

Radius: $$$5$$$A.

Diameter: $$$10$$$A.

Circumference: $$$10 \pi\approx 31.415926535897932$$$A.

Area: $$$25 \pi\approx 78.539816339744831$$$A.

Eccentricity: $$$0$$$A.

Linear eccentricity: $$$0$$$A.

x-intercepts: no x-intercepts.

y-intercepts: $$$\left(0, 6\right)$$$, $$$\left(0, 12\right)$$$A.

Domain: $$$\left[-9, 1\right]$$$A.

Range: $$$\left[4, 14\right]$$$A.