If the divisor of is larger than the divisor of then the major axis is

If the divisor of is larger than the divisor of then

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If the divisor of is larger than the divisor of then the major axis is horizontal along the x -axis, as in Example 1. If the divisor of is larger than the divisor of then the major axis is vertical along the y -axis, as you will see in Example 2. EXAMPLE 2 Graphing an Ellipse with a Vertical Major Axis Graph the ellipse given by Solution: Write the equation in standard form by dividing by 16. Since this ellipse is elongated vertically. and Solve for a and b. and Identify the vertices: and (0, a ). and (0, 4) Identify the x -intercepts on the minor axis: and ( b , 0). and (1, 0) Graph by labeling the points (0, 4), and (1, 0) and connecting them with a smooth curve. YOUR TURN Graph the ellipses: a. b. x 2 9 + y 2 36 = 1 x 2 9 + y 2 4 = 1 ( - 1, 0), (0, - 4), ( - 1, 0) ( - b , 0) (0, - 4) (0, - a ) b = 1 a = 4 b 2 = 1 a 2 = 16 16 7 1, x 2 1 + y 2 16 = 1 16 x 2 + y 2 = 16. x 2 , y 2 y 2 , x 2 (5, 0), (0, - 3), ( - 5, 0), (0, - 3) (0, - b ) ( - 5, 0) ( - a , 0) b = 3 a = 5 b 2 = 9 a 2 = 25 25 7 9, x 2 25 + y 2 9 = 1. x y (0, 3) (–5, 0) (5, 0) (0, –3) Technology Tip Use a graphing calculator to check the graph of Solve for y first. That is, and y 2 = - 3 A 1 - x 2 25 . y 1 = 3 A 1 - x 2 25 x 2 25 + y 2 9 = 1. x y (0, 4) (–1, 0) (1, 0) (0, –4) Answer: a. b. x y (0, 6) (–3, 0) (3, 0) (0, –6) x 2 9 y 2 36 + = 1 x y (0, 2) (–3, 0) (3, 0) (0, –2) x 2 9 y 2 4 + = 1 Study Tip If the divisor of is larger than the divisor of then the major axis is horizontal along the x -axis, as in Example 1. If the divisor of is larger than the divisor of then the major axis is vertical along the y -axis, as you will see in Example 2. x 2 , y 2 y 2 , x 2
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  • Summer '17
  • juan alberto
  • Vertex, MAJOR AXIS, Systems of Nonlinear Equations and Inequalities

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