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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. 284 (page 1157)

In the following exercises, graph each ellipse.
$49 x^{2} + 64 y^{2} = 3136$

Short Answer

Expert verified

The required graph of ellipse is

Step by step solution

01

Step 1. Given Information

The given equation is $49 x^{2} + 64 y^{2} = 3136$

02

Step 2. Calculation

We will first write the equation in standard form.

$\frac{49 x^{2} + 64 y^{2}}{3136} = \frac{3136}{3136} \frac{49 x^{2}}{3136} + \frac{64 y^{2}}{3136} = 1 \frac{x^{2}}{64} + \frac{y^{2}}{49} = 1$

As $64 > 49$ and 64 is in the $x^{2}$ term. So, the major axis is horizontal.

The end points of the major axis.

$a^{2} = 64 a = 卤 \sqrt{64} a = 卤 8$

The end points of major axis are $(- 8, 0) a n d (8, 0)$

The end points of the minor axis.

$b^{2} = 49 b = 卤 \sqrt{49} b = 卤 7$

The end points of minor axis are $(0, - 7) a n d (0, 7)$

03

Step 3. Graph

The graph of ellipse is shown below,

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Most popular questions from this chapter

In the following exercises, simplify each expression using the properties for exponents.

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