Q.124 In the following exercises, (a) ... [FREE SOLUTION]

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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.124 (page 1119)

In the following exercises, (a) write the equation in standard form and (b)graph $4 x^{2} + 25 y^{2} + 8 x + 100 y + 4 = 0$

Short Answer

Expert verified

The required standard equation is $\frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$ $\frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$

Step by step solution

Step 1, Given the information

The given equation of the ellipse is, $4 x^{2} + 25 y^{2} + 8 x + 100 y + 4 = 0$

Part(a): Step 1. Convert the equation into standard form

$4 x^{2} + 25 y^{2} + 8 x + 100 y + 4 = 0 4 x^{2} + 8 x + 25 y^{2} + 100 y + 4 = 0 (p a r i n g) 4 (x^{2} + 2 x) + 25 (y^{2} + 4 y) + 4 = 0 4 (x^{2} + 2 x + 1 - 1) + 25 (y^{2} + 4 y + 4 - 4) + 4 = 0 4 {(x + 1)}^{2} - 4 + 25 {(y + 2)}^{2} - 100 + 4 = 0 4 {(x + 1)}^{2} + 25 {(y + 2)}^{2} = 100 \frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$

Part(a): Step 2. Conclusion

Hence, the required standard equation of the ellipse is $\frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$ localid="1645360637360" $\frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$

Part (b): Step 1, Given the information

The given equation is $\frac{{(x + 1)}^{2}}{25} + \frac{{(y + 2)}^{2}}{4} = 1$

Part (b): Step 2. draw a graph

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

Whose center is $(- 1, - 2)$ and $25 > 4$ , The major axis is horizontal

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91影视

In the following exercises, (a) write the equation in standard form and (b)graph $4 x^{2} + 25 y^{2} + 8 x + 100 y + 4 = 0$

Short Answer

Step by step solution

Step 1, Given the information

Part(a): Step 1. Convert the equation into standard form

Part(a): Step 2. Conclusion

Part (b): Step 1, Given the information

Part (b): Step 2. draw a graph

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91影视

In the following exercises, (a) write the equation in standard form and (b)graph 4x2+25y2+8x+100y+4=0

Short Answer

Step by step solution

Step 1, Given the information

Part(a): Step 1. Convert the equation into standard form

Part(a): Step 2. Conclusion

Part (b): Step 1, Given the information

Part (b): Step 2. draw a graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In the following exercises, (a) write the equation in standard form and (b)graph $4 x^{2} + 25 y^{2} + 8 x + 100 y + 4 = 0$