November 10, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Equation of a circle in standard form.

In this mini-lesson you'll learn, how to find the equation of a circle when it is placed in the coordinate plane. It will be done with the help of some examples, practice questions with solution, and watching video as well as explanation by the instructor in own handwriting.

The equation of a circle in standard form is (*x* - h)^{2} + (*y* - k)^{2} = r^{2}, where (h, k) is the center and r is the radius of a circle. Also, when the center of the circle is (0, 0), and the radius is r, then the equation of a circle is *x*^{2} + *y*^{2} = r^{2}. E.g. if the radius of a circle is 2 with the center at origin, then the equation of the circle is *x*^{2} + *y*^{2} = 4.

You will also find the explanation for finding the coordinates of the center and the radius of a circle from equation of a circle. E.g. to find the center and radius of the circle whose equation is (*x* - 5)^{2} + (*y* - 1)^{2} = 36, relate the equation to the standard form (*x* - h)^{2} + (*y* - k)^{2} = r^{2} and we get h = 5, k = 1 and r = ?36 = 6. Thus, center is (5, 1) and r = 6.

Given the center of a circle (3, -1) and radius 7; to find the equation of the circle we plug in these values in the equation in standard form (*x* - h)^{2} + (*y* - k)^{2} = r^{2}. It works out to (*x* - 3)^{2} + (*y* + 1)^{2} = 49.

In this mini-lesson you'll learn, how to find the equation of a circle when it is placed in the coordinate plane. It will be done with the help of some examples, practice questions with solution, and watching video as well as explanation by the instructor in own handwriting.

The equation of a circle in standard form is (

You will also find the explanation for finding the coordinates of the center and the radius of a circle from equation of a circle. E.g. to find the center and radius of the circle whose equation is (

Given the center of a circle (3, -1) and radius 7; to find the equation of the circle we plug in these values in the equation in standard form (

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.