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# Cha3Cha4-1 - Chapter Three Chapter Four Joy Zhou October 8...

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Chapter Three & Chapter Four Joy Zhou October 8, 2009 Chapter Three 3.1, 3.2, 3.3., 3.4, 3.5, 3.7 Prob 3.1 Note: Definition 3.2.1: ( x - h ) 2 + ( y - k ) 2 = r 2 . (a) h = - 3, k = 4, r = 3. ( x + 3) 2 + ( y - 4) 2 = 9. (b) radius = 1 2 diameter. (c) You basically need to find four centers, because you already know the radius. Any point on the circle centered at (1 , 1) with radius 2 can be a center for the circles you want. For example (3 , 1). To find such points ( x, y ), note the circle centered at (1 , 1) with radius 2 has equation ( x - 1) 2 + ( y - 1) 2 = 4 . (1) Pick any x value for your point, say x = 1, then pug x = 1 into equation (1), solve for the y value. (d) Substitute the x and y values into the equation to see if the equations is satisfied. 1

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For example, for (1 , 1): (1 - 1) 2 + (1 + 1) 2 = 4, so (1 , 1) lies on the graph of this equation. Prob 3.2 Note: the equations in this problem are given in the form of x 2 + ax + y 2 + by + c = 0 , (2) and you are asked to transform them into the form ( x - h ) 2 + ( y - k ) 2 = r 2 (3) to find their centers and radii. The conversion can be done by h = - a/ 2 , k = - b/ 2 , r = h 2 + k 2 - c = ( - a/ 2) 2 + ( - b/ 2) 2 - c. Prob 3.3 Set up the coordinate system as follows. Let the location of the water main be the origin (0 , 0). Let the two crossing streets be the x and y axis. Suppose the runner is running along the x axis towards the water main. Let the unit be in feets. The runner was originally at (6 × 5280 , 0). (convert 6 miles into feets). (a) At time t (t seconds after the water main broke): radius r = 5 t . Run- ner’s new location (31680 - 17 t, 0). The water puddle creates a circle x 2 + y 2 = (5 t ) 2 . (4) Its going to intersect the runner’s path ( x axis) at (5 t, 0). 2
3

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When is 5 t = 31680 - 17 t ? Solve to get t = 24 × 60 sec = 24 min. (b) Now the runner’s running along the straight line y = 5000. This straight line intersects the circle (4) at the point ( x, y ) that satisfies the equation set y = 5000 , x 2 + y 2 = (5 t ) 2 .
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Cha3Cha4-1 - Chapter Three Chapter Four Joy Zhou October 8...

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