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Unformatted text preview: 10.6 Equations of a Circle 10.6
p. 636 Standard equation of a circle Standard
(x-h) + (y-k) = 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 (x-h) + (y-k) = r
2 2 2 (x-(-5)) + (y-0) = 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 (x-h)2 + (y-k)2 = r2 (x-4)2 + (y-(-3))2 = (ð 20)2 (x-4)2 + (y+3)2 = 20 Ex: Graph the circle denoted by the Ex Graph equation (x-3)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 (x-13) +(y-6) =9. Ex
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