Circle Calculator
Solve circles step by step
This calculator will find either the equation of the circle from the given parameters or the center, radius, diameter, circumference (perimeter), area, eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the entered circle. Also, it will graph the circle. Steps are available.
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Your Input
Find the center, radius, diameter, circumference, area, eccentricity, linear eccentricity, x-intercepts, y-intercepts, domain, and range of the circle $$$x^{2} + y^{2} = 9$$$.
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 $$$\left(x - 0\right)^{2} + \left(y - 0\right)^{2} = 3^{2}$$$.
Thus, $$$h = 0$$$, $$$k = 0$$$, $$$r = 3$$$.
The standard form is $$$x^{2} + y^{2} = 9$$$.
The general form can be found by moving everything to the left side and expanding (if needed): $$$x^{2} + y^{2} - 9 = 0$$$.
Center: $$$\left(0, 0\right)$$$.
Radius: $$$r = 3$$$.
Diameter: $$$d = 2 r = 6$$$.
Circumference: $$$C = 2 \pi r = 6 \pi$$$.
Area: $$$A = \pi r^{2} = 9 \pi$$$.
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: $$$\left(-3, 0\right)$$$, $$$\left(3, 0\right)$$$
The y-intercepts can be found by setting $$$x = 0$$$ in the equation and solving for $$$y$$$: (for steps, see intercepts calculator).
y-intercepts: $$$\left(0, -3\right)$$$, $$$\left(0, 3\right)$$$
The domain is $$$\left[h - r, h + r\right] = \left[-3, 3\right]$$$.
The range is $$$\left[k - r, k + r\right] = \left[-3, 3\right]$$$.
Answer
Standard form/equation: $$$x^{2} + y^{2} = 9$$$A.
General form/equation: $$$x^{2} + y^{2} - 9 = 0$$$A.
Graph: see the graphing calculator.
Center: $$$\left(0, 0\right)$$$A.
Radius: $$$3$$$A.
Diameter: $$$6$$$A.
Circumference: $$$6 \pi\approx 18.849555921538759$$$A.
Area: $$$9 \pi\approx 28.274333882308139$$$A.
Eccentricity: $$$0$$$A.
Linear eccentricity: $$$0$$$A.
x-intercepts: $$$\left(-3, 0\right)$$$, $$$\left(3, 0\right)$$$A.
y-intercepts: $$$\left(0, -3\right)$$$, $$$\left(0, 3\right)$$$A.
Domain: $$$\left[-3, 3\right]$$$A.
Range: $$$\left[-3, 3\right]$$$A.