Explanation Graph: Consider the given equation, 4 x 2 + 3 y 2 − 8 x + 18 y + 19 = 0 Rewrite the given equation as a function of y as follows: 4 x 2 + 3 y 2 − 8 x + 18 y + 19 = 0 Write original equation 4 x 2 − 8 x + 3 y 2 + 18 y + 19 = 0 4 x 2 − 2 x + 1 − 4 + 3 y 2 + 6 y + 9 − 27 + 19 = 0 Group terms 4 x − 1 2 + 3 y + 3 2 = 12 Write in completed square form Simplify further, 4 x − 1 2 12 + 3 y + 3 2 12 = 1 Divide by 12 on both sides x − 1 2 3 + y + 3 2 4 = 1 Simplify Rewrite by simplifying above equation as, x − 1 2 3 + y + 3 2 4 = 1 y + 3 2 4 = 1 − x − 1 2 3 Subtracting x − 1 2 3 on both side y + 3 = ± 4 1 − x − 1 2 3 Take square root y = − 3 ± 2 1 − x − 1 2 3 Simplify Now, use graphing calculator TI-83 to graph the above equation as follows, Step1: Press ON key. Step2: Press Y= key. Step3: Enter the equation as, Y 1 = − 3 + 2 1 − X − 1 2 / 3 Y 2 = − 3 − 2 1 − X − 1 2 / 3 Step4: Press WINDOW key. Step5: Now, set the window as shown below, Xmin = − 5 , Xmax = 5 , Xscl = 1 , Ymin = − 5 , Ymax = 5 , Yscl = 1 Step 6: Press GRAPH key. The graph will be displayed as, From the graph, the given ellipse has a vertical major axis with a center at the origin

10th Edition

ISBN: 9781337278461

Author: Ron Larson

Publisher: Cengage Learning

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 6.3, Problem 50E

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To graph: The ellipse, 4x2+3y2−8x+18y+19=0 by using a graphing utility, and also, to determine the center, foci, and vertices.

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Chapter 6.3, Problem 49E

Chapter 6.3, Problem 51E

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To graph: The ellipse, 4 x 2 + 3 y 2 − 8 x + 18 y + 19 = 0 by using a graphing utility, and also, to determine the center, foci, and vertices.

Solution Summary: The author explains how to graph the ellipse and determine the center, foci, and vertices of the given equation.

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To graph: The ellipse, 4x2+3y2−8x+18y+19=0 by using a graphing utility, and also, to determine the center, foci, and vertices.

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Chapter 6 Solutions