50 CHAPTER 1 Graphs To graph the circle, graph the top half ( ) = + − + Y x 2 16 3 1 2 and the bottom half ( ) = − − + Y x 2 16 3 2 2 Also, be sure to use a square screen. Otherwise, the circle will appear distorted. Figure 74 shows the graph on a TI-84 Plus CE. The graph is “disconnected” because of the resolution of the calculator. Geogebra and Desmos do not require that the equation be written in the form { } = y x expression involving . Figure 75 shows the graph of x y 3 2 16 2 2 ( ) ( ) + + − = using Geogebra. Figure 74 ( ) ( ) + + − = x y 3 2 16 2 2 7 23 211 5 16 2 (x 1 3)2 Y 2 5 2 2 16 2 (x 1 3)2 Y 1 5 2 1 Now Work PROBLEMS 29(a) AND (b) Figure 75 Finding the Intercepts of a Circle Find the intercepts, if any, of the graph of the circle ( ) ( ) + + − = x y 3 2 16. 2 2 Solution EXAMPLE 3 This is the equation graphed in Example 2. To find the x-intercepts, if any, let = y 0. Then ( ) ( ) ( ) ( ) ( ) ( ) + + − = + + − = + + = + = + = ± = − ± x y x x x x x 3 2 16 3 0 2 16 3 4 16 3 12 3 12 3 2 3 2 2 2 2 2 2 The x-intercepts are − − ≈ − 3 2 3 6.46 and − + ≈ 3 2 3 0.46. To find the y-intercepts, if any, let = x 0. Then x y y y y y y 3 2 16 0 3 2 16 9 2 16 2 7 2 7 2 7 2 2 2 2 2 2 ( ) ( ) ( ) ( ) ( ) ( ) + + − = + + − = + − = − = − = ± = ± The y-intercepts are − ≈ − 2 7 0.65 and + ≈ 2 7 4.65. y 0 = Simplify. Subtract 4 from both sides. Use the Square Root Method. Solve for x. x 0 = Simplify. Subtract 9 from both sides. Use the Square Root Method. Solve for y.
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