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Standard Equations of Circles. Lesson 9.1A R.4.G.5 Investigate and use the properties of angles ( central and inscribed ) arcs , chords , tangents , and secants to solve problems involving circles

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standard equations of circles

Standard Equations of Circles

Lesson 9.1A

R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

CGT.5.G.4 Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

standard equation of a circle
Standard Equation of a Circle

(x – h)2 + (y – k)2 = r2

h = x coordinate of the center

k = y coordinate of the center

r = radius

example
Example

Write the equation for the circle with the given radius and center

r = 7

Center @ (8, 12)

example 2
Example #2

Write the equation of the circle with the given center and radius

r = √24

Center @ (0, 2)

now you try
Now You Try…

Write the equation of a circle with the given radius and center

r = 16

Center @ (-3, -6)

example1
Example

Write the standard equation of the given circle.

now you try1
Now You Try…

Write the equation of the given circle.

example2
Example

Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph:

(x – 5)2 + (y – 8)2 = 4

example 21
Example #2

Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph:

(x +3 )2 + (y – 7)2 = 8

now you try2
Now You Try…

Find the center and the radius of the circle with the given equation. Give the radius in simplest radical form and graph:

x 2 + (y + 6)2 = 18