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: $$$x^{2} + y^{2} = 9$$$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.
Equation of a circle passing through 3 given points
First point
Second point
Third point
Calculation precision
Digits after the decimal point: 2
Center
Equation of a circle in standard form
Equation of a circle in general form
Parametric equations of a circle
How to find a circle passing through 3 given points
Let's recall how the equation of a circle looks like in
general form:
Since all three points should belong to one circle, we can write a system of equations.
The values
Now we have
three linear equations for three unknowns - system of linear equations with the following matrix form:
We can solve it using, for example, Gaussian elimination like in Gaussian elimination. No solution means that points are co-linear, and it is impossible to draw a circle through them.
The coordinates of a center of a circle and it's radius related to the solution like
this
Knowing center and radius, we can get the equations using Equation of a circle calculator