The following diagram shows how to derive the equation of circle (x - h)2 + (y - k)2 = r2 using Pythagorean Theorem and distance formula. Scroll down the page for examples and solutions.
When working with circle conic sections, we can derive the equation of a circle by using coordinates and the distance formula.
The equation of a circle is (x - h)2 + (y - k)2 = r2 where r is equal to the radius, and the coordinates (x,y) are equal to the circle center.
The variables h and k represent horizontal or vertical shifts in the circle graph.
1. Find the center and the radius
a) x2 + (y + 2)2 = 121
b) (x + 5)2 + (y - 10)2 = 9
2. Find the equation the circle with
a) center(-11, -8) and radius 4
b) center (2, -5) and point on circle(-7, -1)
Identify the equation of a circle.
Write the standard form of a circle from general form.
Graph a circle.
A circle is the set of points (x,y) which are a fixed distance r, the radius, away from a fixed point (h,k), the center.
(x - h)2 + (y - k)2 = r2
1. Graph the circle
a) (x - 3)2 + (y + 2)2 = 16
b) x2 + (y - 1)2 = 4
2. Write in standard form and then graph
2x2 + 2y2 - 12x + 8y - 24 = 0
Introduction to Circles
Understand the equation of a circle
Graph the equation
(x - 1)2 + (y + 2)2 = 9
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