Transcript Sec. 11 – 5 Circles in the Coordinate Plane

Circles in the Coordinate
Plane
Objectives:
1) To write an equation of a circle.
2) To find the center & radius of a
circle.
Equation for a Circle
Thm(11 – 13) An equation of a circle with
center (h, k) & radius (r):
x-coordinate
of center
y-coordinate
of center
(x, y)
r
(h, k)
(x – h)2 + (y – k)2 = r2
Ex.1: Write the Equation of a circle.
Write the standard equation of a circle with
center (-8, 1) and radius of √5.
Graph it.
(x – h)2 + (y – k)2 = r2
(x – (-8))2 + (y – 1)2 = (√5)2
(x + 8)2 + (y – 1)2 = 5
√5
1
-8
Ex.2: Find the center and radius of
a circle with the following equation.
Equation: (x – 4)2 + (y + 2)2 = 25
– Center (4, -2)
– Radius = 5
Ex.3: Graph the circle with the
following Equation
(x + 4)2 + (y – 1)2 = 36
(x – (-4))2 + (y – 1)2 =
– Center: (-4, 1) (√36)2
– Radius: 6
1
-4
2
Ex.4: Write the equation of a circle
from its graph.
(x – h)2 + (y – k)2 = r2
(x – 0)2 + (y – 0)2 = 42
x2 + y2 = 16
4
Ex.4: More Circles
Write the standard equation of a circle with
center (5, 8) & passes through point (-15, -13).
h
k
– Step 1: Solve for r
– Step 2: Put into standard equation
(x – h)2 + (y – k)2 = r2
(-15 – 5)2 + (-13 - 8)2 = r2
x
y
(x – h)2 + (y – k)2 = r2
r2
(x – 5)2 + (y – 8)2 = 292
400 + 441 = r2
(x – 5)2 + (y – 8)2 = 841
-202
+
-212
841 = r2
29 = r
=
What have we learned??
(x – h)2 + (y – k)2 = r2
x-coordinate of a
point on a circle
y-coordinate of a
point on a circle
x-coordinate of the
center of the circle
Radius
y-coordinate of the
center of the circle