Chapter 11: Q.120 (page 1119)

In the following exercises, graph each equation by translation
$\frac{(x + 6^{2})}{16} + \frac{{(y + 5)}^{2}}{4} = 1$

Short Answer

Expert verified

The graph of the ellipse $\frac{{(x + 6)}^{2}}{16} + \frac{{(y + 5)}^{2}}{4} = 1$ is

Step by step solution

Step 1, Given the information

The given equation of the ellipse is $\frac{(x + 6^{2})}{16} + \frac{{(y + 5)}^{2}}{4} = 1$

Step 2. Draw a graph

This ellipse will have the same size and shape as $\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1$

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

Since $16 > 4$ ,The major axis is horizontal

$a^{2} = 16 a = \pm 4$ and $b^{2} = 4 b = \pm 2$

The vertices are $(4, 0) a n d (- 4, 0)$ and The endpoints of the minor axis are $(0, 2) a n d (0, - 2)$

Step 3. Sketch an original graph

The Centre of the ellipse is $(- 6, - 5)$

We translate the graph $\frac{x^{2}}{16} + \frac{y^{2}}{4} = 1$

6 units to the left and then down 5 units.

Verify that the center is $(- 6, - 5)$

Step 4. Conclusion

Hence, the new ellipse is the ellipse whose equation is

$\frac{{(x + 6)}^{2}}{16} + \frac{{(y + 5)}^{2}}{4} = 1$

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In the following exercises, graph each equation by translation
$\frac{(x + 6^{2})}{16} + \frac{{(y + 5)}^{2}}{4} = 1$

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+6216+y+524=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

Decision Maths

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by translation
$\frac{(x + 6^{2})}{16} + \frac{{(y + 5)}^{2}}{4} = 1$