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Chapter 6: Problem 21

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (0,2),(8,2)\(;\) minor axis of length 2

Short Answer

Expert verified
The standard form of the equation of the ellipse is \((x-4)^2/16 + (y-2)^2/1 = 1\)

Step by step solution

01

Derive the Center and the Lengths of the Major and Minor Axes

Firstly, find the midpoint of the given vertices (0,2) and (8,2) to obtain the center of the ellipse, denoted as (h,k). The length of the major axis (2a) is the distance between the vertices, and the length of the minor axis (2b) has been provided.
02

Formulate the Variables a, b, h and k

Calculate the coordinates of the center, \(h\) and \(k\), the length of the semi-major axis \(a\), and the semi-minor axis \(b\). The center is at (4,2), while \(a\) is 4 (half the distance between the vertices) and \(b\) is 1 (half the length of the minor axis).
03

Write the Standard Form of the Equation

Use the obtained values of \(a\), \(b\), \(h\), and \(k\) to write the standard equation of ellipse in the form \((x-h)^2/a^2 + (y-k)^2/b^2 = 1\).

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Most popular questions from this chapter

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