# 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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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 $\left[k - r, k + r\right] = \left[-3, 3\right]$.

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.