 # Equation of Circle

Videos and lessons with examples and solutions to help High School students 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.

Related Topics:
Common Core Geometry
Common Core Mathematics

Common Core: HSG-GPE.A.1

The following figure shows how to derive the equation of a circle. Scroll down the page for more examples and solutions. Equation For a Circle
This lesson shows two examples regarding how to find the equation of a circle centered at the origin.
Examples:
1. Determine an equation for a circle with radius 3 units and centered at the origin.
2. Determine an equation for the circle through the point (-3,4) with center at the origin.
3. Check to see if each of the following points is on, inside or outside the circle for example 2.
a) (2, -3)
b) (1, 5)
c) (-4, -3) Completing the square to write equation in standard form of a circle
Example:
Graph the circle x2 + y2 + 4x - 4y - 17 = 0 Radius and center for a circle equation in standard form.
Example:
The equation of a circle C is (x + 3)2 + (y - 4)2 = 49
What is its center (h, k) and its radius r?

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