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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 of a Circle

Equation For a Circle
This lesson shows two examples regarding how to find the equation of a circle centered at the origin.
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
Graph the circle x2 + y2 + 4x - 4y - 17 = 0 Radius and center for a circle equation in standard form.
The equation of a circle C is (x + 3)2 + (y - 4)2 = 49
What is its center (h, k) and its radius r?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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