Circle Calculator

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.

Related calculators: Parabola Calculator, Ellipse Calculator, Hyperbola Calculator, Conic Section Calculator

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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: $$$x^{2} + y^{2} = 9$$$A.

General form: $$$x^{2} + y^{2} - 9 = 0$$$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.