Properties of the circle $$$x^{2} + y^{2} = 16$$$
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Find the center, radius, diameter, circumference, area, eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the circle $$$x^{2} + y^{2} = 16$$$.
Solution
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.
Our circle in this form is $$$\left(x - 0\right)^{2} + \left(y - 0\right)^{2} = 4^{2}$$$.
Thus, $$$h = 0$$$, $$$k = 0$$$, $$$r = 4$$$.
The standard form is $$$x^{2} + y^{2} = 16$$$.
The general form can be found by moving everything to the left side and expanding (if needed): $$$x^{2} + y^{2} - 16 = 0$$$.
Center: $$$\left(0, 0\right)$$$.
Radius: $$$r = 4$$$.
Diameter: $$$d = 2 r = 8$$$.
Circumference: $$$C = 2 \pi r = 8 \pi$$$.
Area: $$$A = \pi r^{2} = 16 \pi$$$.
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: $$$\left(-4, 0\right)$$$, $$$\left(4, 0\right)$$$
The y-intercepts can be found by setting $$$x = 0$$$ in the equation and solving for $$$y$$$: (for steps, see intercepts calculator).
y-intercepts: $$$\left(0, -4\right)$$$, $$$\left(0, 4\right)$$$
The domain is $$$\left[h - r, h + r\right] = \left[-4, 4\right]$$$.
The range is $$$\left[k - r, k + r\right] = \left[-4, 4\right]$$$.
Answer
Standard form/equation: $$$x^{2} + y^{2} = 16$$$A.
General form/equation: $$$x^{2} + y^{2} - 16 = 0$$$A.
Graph: see the graphing calculator.
Center: $$$\left(0, 0\right)$$$A.
Radius: $$$4$$$A.
Diameter: $$$8$$$A.
Circumference: $$$8 \pi\approx 25.132741228718346$$$A.
Area: $$$16 \pi\approx 50.265482457436692$$$A.
Eccentricity: $$$0$$$A.
Linear eccentricity: $$$0$$$A.
x-intercepts: $$$\left(-4, 0\right)$$$, $$$\left(4, 0\right)$$$A.
y-intercepts: $$$\left(0, -4\right)$$$, $$$\left(0, 4\right)$$$A.
Domain: $$$\left[-4, 4\right]$$$A.
Range: $$$\left[-4, 4\right]$$$A.