Chapter 11: Q.119 (page 1119)

In the following exercises, graph each equation by translation $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$

Short Answer

Expert verified

The graph of the ellipse is $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$

Step by step solution

Step 1, Given the information

The given equation of the ellipse is $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$

Step 2. Draw a graph

This ellipse will have the same size and shape as $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$

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

Since localid="1645263510312" $4 < 25$ The major axis is vertical,

localid="1645264360187" $a^{2} = 4 a = \pm 2$ and localid="1645264389332" $b^{2} = 25 b = \pm 5$

The vertices arelocalid="1645264420538" $(0, 5), (0, - 5)$ and The endpoints of the minor axis arelocalid="1645264454889" $(2, 0), (- 2, 0)$

Step 3. Sketch an original graph

The Centre of the ellipse is $(3, 7)$

We translate the graph $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$

3 units to the right and then up 7 units.

Verify that the center is $(3, 7)$

Step 4. Conclusion

Hence, the new ellipse is the ellipse whose equation is $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises, graph each equation by translation $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Decision Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by translationx-324+y-7225=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

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Decision Maths

Probability and Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by translation $\frac{{(x - 3)}^{2}}{4} + \frac{{(y - 7)}^{2}}{25} = 1$