Chapter 11: Q.121 (page 1119)

In the following exercises, graph each equation by translation $\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$

Short Answer

Expert verified

The graph of the ellipse $\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$

Step by step solution

Step 1, Given the information

The given equation of the ellipse is $\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$

Step 2. Draw a graph

This ellipse will have the same size and shape as $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$

Whose center is $(0, 0)$ Firstly we plot this graph,

Since $9 < 25$ The major axis is vertical,

$a^{2} = 9 a = \pm 3$ and $b^{2} = 25 b = \pm 5$

The vertices are $(0, 5), (0, - 5)$ and The endpoints of the minor axis are $(3, 0), (- 3, 0)$

Step 3. Sketch an original graph

The Centre of the ellipse is $(5, - 4)$

We translate the graph $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$

5 units to the right and then down 4 units.

Verify that the center is $(5, - 4)$

Step 4. Conclusion

Hence, the new ellipse is the ellipse whose equation is

$\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$

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In the following exercises, graph each equation by translation $\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$

Short Answer

Step by step solution

Step 1, Given the information

Step 2. Draw a graph

Step 3. Sketch an original graph

Step 4. Conclusion

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In the following exercises, graph each equation by translationx-529+y+4225=1

Short Answer

Step by step solution

Step 1, Given the information

Step 2. Draw a graph

Step 3. Sketch an original graph

Step 4. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Probability and Statistics

Pure Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by translation $\frac{{(x - 5)}^{2}}{9} + \frac{{(y + 4)}^{2}}{25} = 1$