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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. 283 (page 1157)

In the following exercises, graph each ellipse.
$\frac{x^{2}}{4} + \frac{y^{2}}{81} = 1$

Short Answer

Expert verified

The required graph of ellipse is

Step by step solution

01

Step 1. Given Information

The given equation is $\frac{x^{2}}{4} + \frac{y^{2}}{81} = 1$

02

Step 2. Explanation

We will first determine whether the major axis is horizontal or vertical.

As $81 > 4$ and 81 is in the $y^{2}$ term, so the major axis is vertical.

The end points of the major axis.

$b^{2} = 81 b = 卤 \sqrt{81} b = 卤 9$

The end points of major axis are $(0, - 9) a n d (0, 9)$

The end points of the minor axis.

$a^{2} = 4 a = 卤 \sqrt{4} a = 卤 2$

The end points of minor axis are $(- 2, 0) a n d (2, 0)$

03

Step 3. Graph

The graph of ellipse is shown below,

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Most popular questions from this chapter

Multiply $\frac{3 {xy}^{2}}{8 y^{3}} . \frac{16 y^{2}}{24 x}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{27 p^{2} q}{108 p^{4} q^{3}}}$

(b) $\sqrt[3]{\frac{16 c^{5} d^{7}}{250 c^{2} d^{2}}}$

(c) $\sqrt[6]{\frac{2 m^{9} n^{7}}{128 m^{3} n}}$

Explain why an equation of the form $\sqrt{x} + 1 = 0$ has no solution.

Solve $25 p^{2} = 49$ $25 p^{2} = 49$

In the following exercises, factor completely

$24 a^{4} - 9 a^{3}$ .

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