c. tion set is h 135 Section 1.2 Circles ts fy the Practice Exercises Prerequisite Review For Exercises R. 1-R.2, find the value of n so that the expression is a perfect square trinomial. Then factor the trinomial. SECTION 1.2 2 R.4. Multiply by using the special case products. Simplify. (x 2)2 R.2. x are. Note 8c +n R.1. c . (x-0f. R.3. Find the distance between (2, 3) and (-3, -2). Express your answer in simplified radical form. Concept Connections 1. A r. and is often denoted by is the set of all points in a plane equidistant from a fixed point called the ual 3. The standard form of an equation of a circle with center (h, k) and radius r is given by 4. An equation of a circle written in the form x y2+ Ax +By + C = 0 is called the equation of a circle. form of an 2. The distance from the center of a circle to any point on the circle is called the Objective 1: Write an Equation of a Circle in Standard Form 6. Is the point (3, 5) on the circle defined by 5. Is the point (2, 7) on the circle defined by (x 2) (- 7)24? 3)2 y5) 36? (x 8. Is the point (2, -7) on the circle defined by (x 6)2(y + 1)2 100? 7. Is the point (-4, 7) on the circle defined by (x +1) - 3)2= 25? For Exercises 9-16, determine the center and radius of the circle. 10. (x 3) (y 11. 2(y2.5)2= 6.25 14. y 28 1)2 16 (y + 2) 81 9. (x4) 13. xy20 + 2.25 12. (x 1.5) + y 25 -) 3 81 3 x + 16. 9 5 1 + 15. 49 2 For Exercises 17-32, information about a circle is given. a. Write an equation of the circle in standard form. b. Graph the circle. (See Examples 1-2) 18. Center: -3, 2); Radius: 4 17. Center: (-2, 5); Radius: 1 otr 20. Center: (6, -2); Radius: 6 19. Center: (4, 1); Radius: 3 22. Center: (-5, -2); Radius: V21 21. Center: (-4, -3); Radius: V11 24. Center: (0, 0); Radius: 4.2 23. Center: (0, 0); Radius: 2.6 26. The endpoints of a diameter are (7, 3) and (5, -1). 25. The endpoints of a diameter are (-2, 4) and (6, -2). 28. The center is (3, 1) and another point on the circle is (6, 5). 27. The center is (-2, -1) and another point on the circle is (6, 5), 30. The center is (-2, -4) and the circle is tangent to t x-axis. 29. The center is (4, 6) and the circle is tangent to the y-axis. (Informally, a line is tangent to a circle if it touches the circle in exactly one point.) 32. The center is in Quadrant II, the radius is 3, and t circle is tangent to both the x- and y-axes. 31. The center is in Quadrant IV, the radius is 5, and the circle is tangent to both the x- and y-axes. 34. Write an equation that represents the set of point are 9 units from (-4, 16). 33. Write an equation that represents the set of points that are 5 units from (8, -11). 36. Write an equation of the circle that is tangent to axes with radius V11 and center in Quadrant I 35. Write an equation of the circle that is tangent to both axes with radius V7 and center in Quadrant I.