To draw the ellipse shown in the figure, you need to derive the expressions for the x and y coordinates of the boundary points in parametric equations. (a) Derive the expression for the ellipse that is located at the origin and oriented with its major axis in the x direction. (b) Apply the proper transformations to the expression derived in (a) to get the parametric equation of the ellipse shown. Y 5 3 30⁰ X Figure 1 Ellipse Location and Orientation

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 36E
Question

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1. To draw the ellipse shown in the figure, you need to derive the expressions for the
x and y coordinates of the boundary points in parametric equations.
(a) Derive the expression for the ellipse that is located at the origin and oriented
with its major axis in the x direction.
(b) Apply the proper transformations to the expression derived in (a) to get the
parametric equation of the ellipse shown.
Y
5
3
2
30⁰
X
Figure 1 Ellipse Location and Orientation
Transcribed Image Text:1. To draw the ellipse shown in the figure, you need to derive the expressions for the x and y coordinates of the boundary points in parametric equations. (a) Derive the expression for the ellipse that is located at the origin and oriented with its major axis in the x direction. (b) Apply the proper transformations to the expression derived in (a) to get the parametric equation of the ellipse shown. Y 5 3 2 30⁰ X Figure 1 Ellipse Location and Orientation
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