Lesson 12-7: Circles in th Coordinate Plane
Objectives:
Write equations and graph circles in the coordinate plane.
Use the equation and graph of a circle to solve problems.
If you are given the equation of a circle, you can graph the
circle by identifying its center and radius.
Graph x2 + y2 = 16.
The equation of a circle is based on the Distance Formula
and the fact that all points on a circle are equidistant from
the center.
Graph (x – 3)2 + (y + 4)2 = 9.
Write the equation of each circle.
J with center J (2, 2) and radius 4
K that passes through J(6, 4) and has center K(1, –8)
Graph (x – 3)2 + (y + 2)2 = 4.
P with center P(0, –3) and radius 8
Q that passes through (2, 3) and has center Q(2, –1)
An amateur radio operator wants to build a radio
antenna near his home without using his house as a
bracing point. He uses three poles to brace the antenna.
The poles are to be inserted in the ground at three points
equidistant from the antenna located at J(4, 4), K(–3, –1),
and L(2, –8). What are the coordinates of the base of the
antenna?
Crater Lake in Oregon is a roughly circular lake. The lake
basin formed about 7000 years ago when the top of a
volcano exploded in an immense explosion. Hillman
Peak, Garfield Peak, and Cloudcap are three mountain
peaks on the rim of the lake. The peaks are located in a
coordinate plane at H(-4, 1), G(-2, -3), and C(5, -2).
Find the coordinates of the center of the lake.
Each unit of the coordinate plane represents
Find the diameter of the lake.
3
mile.
5