Find circle given the center $$$\left(-3, -5\right)$$$, the radius $$$6$$$

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, $$$h = -3$$$, $$$k = -5$$$, $$$r = 6$$$.

The standard form is $$$\left(x + 3\right)^{2} + \left(y + 5\right)^{2} = 36$$$.

The general form can be found by moving everything to the left side and expanding (if needed): $$$x^{2} + 6 x + y^{2} + 10 y - 2 = 0$$$.

Diameter: $$$d = 2 r = 12$$$.

Circumference: $$$C = 2 \pi r = 12 \pi$$$.

Area: $$$A = \pi r^{2} = 36 \pi$$$.

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).

x-intercepts: $$$\left(- \sqrt{11} - 3, 0\right)$$$, $$$\left(-3 + \sqrt{11}, 0\right)$$$

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

y-intercepts: $$$\left(0, - 3 \sqrt{3} - 5\right)$$$, $$$\left(0, -5 + 3 \sqrt{3}\right)$$$

The domain is $$$\left[h - r, h + r\right] = \left[-9, 3\right]$$$.

The range is $$$\left[k - r, k + r\right] = \left[-11, 1\right]$$$.

Standard form/equation: $$$\left(x + 3\right)^{2} + \left(y + 5\right)^{2} = 36$$$A.

General form/equation: $$$x^{2} + 6 x + y^{2} + 10 y - 2 = 0$$$A.

Graph: see the graphing calculator.

Center: $$$\left(-3, -5\right)$$$A.

Radius: $$$6$$$A.

Diameter: $$$12$$$A.

Circumference: $$$12 \pi\approx 37.699111843077519$$$A.

Area: $$$36 \pi\approx 113.097335529232557$$$A.

Eccentricity: $$$0$$$A.

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

x-intercepts: $$$\left(- \sqrt{11} - 3, 0\right)\approx \left(-6.3166247903554, 0\right)$$$, $$$\left(-3 + \sqrt{11}, 0\right)\approx \left(0.3166247903554, 0\right)$$$A.

y-intercepts: $$$\left(0, - 3 \sqrt{3} - 5\right)\approx \left(0, -10.196152422706632\right)$$$, $$$\left(0, -5 + 3 \sqrt{3}\right)\approx \left(0, 0.196152422706632\right)$$$A.

Domain: $$$\left[-9, 3\right]$$$A.

Range: $$$\left[-11, 1\right]$$$A.