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Unformatted text preview: 10.6 Equations of a Circle 10.6
p. 636 Standard equation of a circle Standard
(xh) + (yk) = r
2 2 2 r = radius length (h,k) = coordinates of the center point (x,y) represents the ordered pairs for (x,y) every point on the circle. every on Ex: Write the standard equation of a Ex Write circle with center (5,0) and a radius of 4.8. of (xh) + (yk) = r
2 2 2 (x(5)) + (y0) = 4.8
2 2 2 (x+5) + y = 23.04
2 2 The point (2,1) is on a circle whose center is (4,3). Write the standard equation of the circle. equation
We need the radius length. Use distance formula from center to the Use pt. on the circle to find the radius. pt. r = ð 20 (xh)2 + (yk)2 = r2 (x4)2 + (y(3))2 = (ð 20)2 (x4)2 + (y+3)2 = 20 Ex: Graph the circle denoted by the Ex Graph equation (x3)2 + (y+1)2 = 4. equation
Center? (3,1) Radius? r = ð4 = 2 To graph: * Graph the center pt. 1 .
st * Use radius length to get Use 4 pts. on the circle. (one above, below, to left & right) above, * Do your best to draw a Do Ex: The equation of a circle is (x13) +(y6) =9. Ex
2
2 Three points are located as follows: A(5,6), B(14,8), & C(20,9). Which pt. is in the circle? B(14,8), • There are 2 ways to approach this problem. There ways • The first is to realize that the radius of the given circle is 3. given • This means the distance from the center to This any point on the circle should be 3. any • If you find the distance from the center to If one of the given points and it is smaller than 3, then that point must be inside the circle. • If the distance is greater than 3, then that If point must be outside the circle. point Go ahead; find the distances. Go
Distance from A(5,6) to center (13,6)? Distance from B(14,8) to center (13,6)? Distance from C(20,9) to center (13,6)? So which point is inside the circle? B The second way to approach this problem is to graph the circle, then graph the 3 points. graph C B A Assignment Assignment ...
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 Spring '08
 GERMAN
 Equations

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