Exercises Involving Distance and Circles
1. The distance between points (a,b) and (c,d) is ___________________.
2. The circle with radius r and center at the point (h,0) is given by the equation _______________.
3. The circle with radius r and center at the point (0,k) is given by the equation _______________.
For exercises 4 through 6, answer true or false and explain your reasoning.
4. A circle is never the graph of a function.
5. If the distance between the point P and the point (3,4) is 5, then P must be the origin.
6. Let P and Q be two points that lie on a circle and let C be the center of the circle. If the distance between C and P is 7, then the distance between C and Q must also be 7.
For exercises 7 through 16, find the distance between the points P and Q.
7. P = (0,0) and Q = (4,3)
8. P = (0,0) and Q = (12,6)
9. P = (1,-3) and Q = (7,-11)
10. P = (-2,-5) and Q = (0,-5)
11. P = (a,4) and Q = (a + 2, 3)
12. P = (3, a) and Q = (5, a - 6)
13. P = (a,b) and Q = (b,a)
14. P = (u, u + v) and Q = (u - v, v)
15. P = (1,2) and Q is the intersection of the lines 2x + y = 7 and 5x - 2y = 4.
16. P = (4,5) and Q is the intersection of the lines 4x - 3y = 10 and 13x + 6y = 1.
17. P = (-2,1) and Q is the y-intersect of the line 3x + 2y = 1.
For exercises 18 through 21, find the equation of the circle with the given center and radius.
18. Center (0,0) and radius 2.
19. Center (0,0) and radius 5.
20. Center (-1,5) and radius 7.
21. Center (2,-4) and radius 3.
For exercises 22 through 32, find the center and radius of the given circle. Then sketch the graph.
22. x2 + y2 = 16
23. 4x2 + 4y2 = 1
24. (x - 1)2 + y2 = 25
25. (x - 2)2 + (y + 1)2 = 49
26. (x - 2)2 + (y + 1)2 = 1
27. (x + 2)2 + (y - 2)2 = 4
28. (x - 1)2 + (y - 3)2 = 5
29. (x + 2)2 + (y + 1)2 = 2
30. x2 + y2 + 2y = 0
31. x2 + y2 + 6x = 7
32. x2 + y2 + 4x + 2y = 5
33. x2 + y2 = 2x + 8
34. x2 + y2 = 2x + 10y - 25
For exercise 35 through 37 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).
36. The circle with center (-1,1) that contains the point (-2, -4).
37. The circle with radius 3 that contains the points (-1, 2) and (-1, 8).
38. The circle with radius 1 that contains the points (3,-2) and (5,-2).
For exercises 39 through 42, find the equation of the circle.
39. 
40. 
41. 
42. 
43. 
44. 
45. Center at (0,0) and passes through the point (0,4).
46. Center at (0,0) and passes through the point (-3,0).
47. Center at (0,0) and passes through the point (2,4).
48. Center at (0,0) and passes through the point (-3,1).
49. Center at (3,1) and passes through the point (4,5).
50. Center at (-1,3) and passes through the point (2,-4).