Exercises Involving Distance and Circles

1.  The distance between points (a,b) and (c,d) is .

3.  The circle with radius r and center at the point (0,k) is given by the equation x2 + (y - k)2  =  r2.

5.  If the distance between the point P and the point (3,4) is 5, then P must be the origin.  

False, P could be any point on the circle with radius 5 and center (3,4).

7.  P  =  (0,0) and Q  =  (4,3)

The distance is 5.

9.  P  =  (1,-3) and Q  =  (7,-11)

The distance is 10.

11.  P  =  (a,4)  and Q  =  (a + 2, 3)

The distance is

13.  P  =  (a,b) and Q  =  (b,a)

The distance is  

15.  P  =  (1,2) and Q is the intersection of the lines 2x + y = 7 and 5x - 2y = 4.

The distance is

17.  P  =  (-2,1) and Q is the y-intersect of the line 3x + 2y  =  1.

The distance is

19.  Center (0,0) and radius 5.

    x2 + y2  =  25

21.  Center (2,-4) and radius 3.

    (x - 2)2 + (y + 4)2  =  9

23.  4x2 + 4y2  =  1

Center:  (0,0) Radius:  1/2

25.  (x - 2)2 + (y + 1)2  =  49

Center:  (2,-1)  Radius:  7

27.  (x + 2)2 + (y - 2)2  =  4

Center:  (-2,2)  Radius:  2

29.  (x + 2)2 + (y + 1)2  =  2

Center:  (-2,-1)  Radius: 

31.  x2 + y2 + 6x  =  7

Center:  (-3,0)  Radius:  4

33.  x2 + y2  =  2x + 8

Center:  (1,0)  Radius:  3

For exercise 33 through 36 find equation of the circle with the given information.  Then sketch the graph.

35.  The circle with center (3, -2) that contains the point (6, 2).

        (x - 3)2 + (y + 2)2  =  25

37.  The circle with radius 3 that contains the points (-1, 2) and (-1, 8).

        (x + 1)2 + (y - 5)2  =  9

For exercises 37 through 40, find the equation of the circle.

39.      

        x2 + y2  =  9

41.      

        (x - 3)2 + (y - 2)2  =  4

43.    

        (x - 3)2 + (y + 3)2  =  1

45.  Center at (0,0) and passes through the point (0,4).

        x2 + y2  =  16

47.  Center at (0,0) and passes through the point (2,4).

        x2 + y2  =  20

49.  Center at (3,1) and passes through the point (4,5).

        (x - 3)2 + (y - 1)2  =  17

 


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