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Graphing Ellipses

March 29, 2024 by admin Category: Top

You are viewing the article Graphing Ellipses  at Tnhelearning.edu.vn you can quickly access the necessary information in the table of contents of the article below.

How to Graph Ellipses and Write the Equation
How to Graph Ellipses and Write the Equation

Graphing Ellipses

Now we will take this information and use it to graph an ellipse.

Before we do that, though, let’s review the patterns:

To graph an ellipse:

1. Find and graph the center point.
2. Determine if the ellipse is vertical or horizontal and the a and b values.
3. Use the a and b values to plot the ends of the major and minor axis.
4. Draw in the ellipse.

2. Determine if the ellipse is vertical or horizontal and the a and b values.

3. Use the a and b values to plot the ends of the major and minor axis.

4. Draw in the ellipse.

Let’s graph a couple, and you’ll see how it works.

First we must identify the center point, which is (2, -1). (Remember that you must take the opposite of each number inside the parenthesis.) Let’s graph that point:

  Writing the Equation of an Ellipse

Now we need to determine if the ellipse is vertical or horizontal. Since the larger number is under the x, we know it is horizontal. Remember to find a and b, we have to take the square roots of the denominators. So a = 4 and b = 3.

We can now use a and b to plot the ends of the major and minor axis. This parabola is horizontal and the a value (4) is the distance from the center point to the end of the major axis. Since the major axis is horizontal, we’ll count right 4 and left 4 to plot its endpoints.

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Now we’ll use the b value (3) to find the ends of the minor axis. Let’s count up 3 blocks and down 3 blocks and plot the points there.

To finish, we simply need to draw in the ellipse.

Once again, the center point is not technically part of the answer, so a technical graph would look like this:

  Graphs of Ellipses


First we must identify the center point, which is (-3, 4). Let’s graph it:

Now we need to determine if the ellipse is vertical or horizontal. Since the larger number is under the y, we know it is vertical. Remember to find a and b, we have to take the square roots of the denominators. So a = 5 and b = 2.

We must now use a and b to plot the ends of the major and minor axis. This parabola is vertical and the a value (5) is the distance from the center point to the end of the major axis. Since the major axis is vertical, we’ll count up 5 and down 5 to plot its endpoints.

Now we’ll use the b value (2) to find the ends of the minor axis. Let’s count left 2 blocks and right 2 blocks and plot the points there.

To finish, we simply need to draw in the ellipse.

Practice: Graph each ellipse.





Answers:

  Ellipse Graph Explained with Equations and Solved Examples





Related Links:

Math

Fractions

Factors

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