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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q.122 (page 1119)

In the following exercises, graph each equation by translation $\frac{{(x + 5)}^{2}}{36} + \frac{{(y - 3)}^{2}}{16} = 1$

Short Answer

Expert verified

The graph of the ellipse $\frac{{(x + 5)}^{2}}{36} + \frac{{(y - 3)}^{2}}{16} = 1$

Step by step solution

01

Step 1, Given the information

The given equation of the ellipse is $\frac{{(x + 5)}^{2}}{36} + \frac{{(y - 3)}^{2}}{16} = 1$

02

Step 2. Draw a graph

This ellipse will have the same size and shape as $\frac{x^{2}}{36} + \frac{y^{2}}{16} = 1$

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

Since The major axis is horizontal

$a^{2} = 36 a = 卤 6$ and $b^{2} = 16 b = 卤 4$

The vertices are $(6, 0) a n d (- 6, 0)$ and The endpoints of the minor axis are $(0, 4), (0 - 4)$

03

Step 3. Sketch an original graph

The Centre of the ellipse is $(- 5, 3)$

We translate the graph $\frac{x^{2}}{36} + \frac{y^{2}}{16} = 1$

5 units to the left and then up 3 units.

Verify that the center is $(- 5, 3)$

04

Step 4. Conclusion

Hence, the new ellipse is the ellipse whose equation is $\frac{{(x + 5)}^{2}}{36} + \frac{{(y - 3)}^{2}}{16} = 1$

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Most popular questions from this chapter

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{4}{(x - 2)} 鈮� \frac{3}{(x + 1)}$

In the following exercises, solve each rational inequality and write the solution in interval notation.

$\frac{1}{2} - \frac{4}{x^{2}} 鈮� \frac{1}{x}$

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Part (b): $\sqrt{3 b}$

Part (c): $\sqrt[8]{40 c}$

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Solve quadratic equations by factoring.

$3 y^{3} + 48 y = 24 y^{2}$

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