Embed Size (px)
DESCRIPTION
Examples (1) – (5) Determine the center and radius of the circle having the given equation. Identify four points of the circle.
Citation preview
The Circle
222 )()(
:
),(
rkyhx
formdardntastheincircleaofequationTherRadiuskhCenter
Examples (1) – (5)
Determine the center and radius of the circle having the given equation. Identify four points of the circle.
1684.5
3)2()1(.4
1)2(.3
4)1(.2
9.1
22
22
22
22
22
yxyx
yx
yx
yx
yx
Solutions
)0,3(),0,3(),3,0(),3,0(:
39
)0,0(9)0()0(
9.122
22
circletheonntsPoiradius
centeryx
yx
)0,3(),0,1(),2,1(),2,1(:
24
)0,1(4)0())1((
4)1(.222
22
circletheonntsPoiradius
centeryx
yx
)2,1(),2,1(),1,0(),3,0(:
11
)2,0(1)2()0(
1)2(.322
22
circletheonntsPoiradius
centeryx
yx
)2,31(),2,31(),32,1(),32,1(
:3
)2,1(3))2(()1(
3)2()1(.422
22
circletheonntsPoiradius
centeryx
yx
)4,8()4,62(),4,4()4,62(,)2,2()64,2(),10,2()64,2(
:636
)4,2(36)4())2((
36)4()2(
1616)4(4)2(
1684
1684.5
22
22
22
22
22
circletheonntsPoiradius
centeryx
yx
yx
yyxx
yxyx
EXAMPLE (6)
Find the equation of the circle with radius 4 and center at (3, -2)
16)2()3(
4))2(()3(
4)2,3(
22
222
yx
yx
circletheofEquationradiuscenter
Solution
EXAMPLE (7)Find the radius and center of each of the following circles:1.. 9x2+ 9y2 = 92.. 9x2+ 9y2 = 9003.. 9x2+ 9y2 = 254.. 3(x+2)2+ 3y2 = 275.. 2x2+ 2(y-1)2 = 86.. 2(x-5)2+ 2(y+1)2 = 4
35
925)0,0(
)9(925 x
259x9 3.
10010)0,0(
)9(001 x
9009x9 2.
11)0,0(
)9(1 x
99x9 1.
22
22
22
22
22
22
randCenter
byDividingy
y
randCenter
byDividingy
y
randCenter
byDividingy
y
2)1,5(
2)1()5(
4)1(2)5(2 6.
24)1,0(
)2(4)1(
8)1(22 5.
39)0,2(
)3(9)2(
273)2(3 4.
22
22
22
22
22
22
randCenter
yx
yx
randCenter
byDividingyx
yx
randCenter
byDividingyx
yx
