Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Obj. 60 Circles in the Coordinate Plane
1. Obj. 60 Circles in the Coordinate Plane
The student is able to (I can):
• Write equations and graph circles in the coordinate plane
• Use the equation and graph of a circle to solve problems.
2. The equation of a circle is based on the
Distance Formula.
(h, k)
(x, y)
r
( ) ( )
2 2
2 1 2 1d x x y y= − + −
( ) ( )22
kyhr x= − + −
( ) ( )22 2
x h y k r− + − =
3. Examples Identify the center and radius of the
circles.
1.
center: (7, 2); radius:
2.
center: (—5, 1); radius:
3.
center: (0, —3); radius:
( ) ( )22
x 7 y 2 16− + − =
16 4=
( ) ( )22
x 5 y 1 36+ + − =
36 6=
( )22
x y 3 20+ + =
20 2 5=
4. To graph a circle once you know its center
and radius:
• Plot its center
• Count the radius from the center up,
down, left, and right.
• Draw a smooth curve connecting the
four points.
You can also use a compass. Plot the
center as before, open up the compass to
the length of the radius, and then draw the
circle.
5. Examples Write the equation of each circle.
1. A with center A(4, —2) and radius 3
2. B with center B(—6, 3) that passes
through (—2, 6)
( ) ( )( )
22 2
x 4 y 2 3− + − − =
h k
( ) ( )22
x 4 y 2 9− + + =
h k
x y
( )( ) ( )
2 2 2
2 66 3 r− + −−− =
2
25 r=
( ) ( )22
x 6 y 3 25+ + − =
