Answer the problems and provide clear and understandable solution. Also, there is an answer below, you just need to provide the the complete colution.

Example 1.1.1. In each item, give the standard equation of the circle satisfying the given conditions. (1) center at the origin, radius 4 (2) center (-4,3), radius v7 12 (3) circle in Figure 1.7 (4) circle A in Figure 1.9 (5) circle B in Figure 1.9 (6) center (5, -6), tangent to the y-axis (7) center (5. -6), tangent to the r-axis (8) has a diameter with endpoints A(-1, 4) and B(4, 2) B 3- N X 6 -5 -4 -3 -2 -1 0 3 4. 6 NO Figure 1.9 Solution. (1) a3 + y' = 16 (2) (2 + 4)3 + (1 - 3) =71.1.2. Definition and Equation of a Circle A circle may also be considered a special kind of ellipse (for the special case when the tilted plane is horizontal). For our purposes, we will distinguish between these two conics. 11 See Figure 1.7, with the point C(3, 1) shown. From the figure, the distance of A(-2, 1) from C is AC = 5. By the distance formula, the distance of B(6, 5) from C is BC = /(6 - 3)3 + (5 -1)? = 5. There are other points P such that PC = 5. The collection of all such points which are 5 units away from C, forms a circle. -6 -4 10 1 2 Figure 1.7 Figure 1.8 Let C be a given point. The set of all points P having the same distance from C is called a circle. The point C is called the center of the circle, and the common distance its radius