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 Calculator is a free online tool that displays the equation of a circle of a given input. BYJU’S online equation of a circle calculator tool makes the calculation faster, and it displays the equation in a fraction of seconds.
How to Use the Equation of a Circle Calculator?
The procedure to use the equation of a circle calculator is as follows:
Step 1: Enter the circle centre and radius in the respective input
field
Step 2: Now click the button “Find Equation of Circle” to get the equation
Step 3: Finally, the equation of a circle of a given input will be displayed in the new window
What is the Equation of a Circle?
In geometry, a circle is a two-dimensional round shaped figure where all the points on the surface of the circle are equidistant from the centre point (c). The distance from the centre of the circle to the surface is called the radius (R). The equation
of a circle can be calculated if the centre and the radius are known. Thus the equation of a circle is given by
(x-h)2 +(y-k)2 = r2
Where
(h, k) – centre coordinates
r – radius