Stitz-Zeager_College_Algebra_e-book

One way to describe the solution set to this system

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Unformatted text preview: o a2 = 9. All that remains is to find b2 . To that end, we use the fact that c = 1 to get 424 Hooked on Conics √ c= a2 − b2 √ 1= 9 − b2 √ 9 − b2 12 = 2 1 = 9 − b2 b2 = 8 Substituting all of our findings into the equation to be (x − 3)2 (y − 1)2 + = 1. 9 8 (x − h)2 (y − k )2 + = 1, we get our final answer a2 b2 As with circles and parabolas, an equation may be given which is an ellipse, but isn’t in the standard form of Equation 7.4. In those cases, as with circles and parabolas before, we will need to massage the given equation into the standard form. To Write the Equation of an Ellipse in Standard Form 1. Group the same variables together on one side of the equation and position the constant on the other side. 2. Complete the square in both variables as needed. 3. Divide both sides by the constant term so that the constant on the other side of the equation becomes 1. Example 7.4.3. Graph x2 + 4y 2 − 2x + 24y + 33 = 0. Find the center, the lines which contain the major and minor axes, the vertices, and the foci. Solut...
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