Equations of ellipses and hyperbolas Find an equation of the following ellipses and hyperbolas, assuming the center is at the origin. An ellipse whose major axis is on the x-axis with length 8 and whose minor axis has length 6

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter7: Conic Sections And Quadratic Systems
Section7.2: The Ellipse
Problem 1SC: Self Check Find an equation in the standard form of the ellipse with center at the origin, major...
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Equations of ellipses and hyperbolas Find an equation of the following ellipses and hyperbolas, assuming the center is at the origin.

An ellipse whose major axis is on the x-axis with length 8 and whose minor axis has length 6

Expert Solution
Step 1

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

To find the equation by assuming the center is at the origin

x-axis with length 8 and minor axis has length 6

Given:

2a=8

a=4

And 

2b=6

b=3

 

Step 3

Hence an equation of the required ellipse is x216+y29=1

Vertices are ±a,0=±4,0±7,0

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