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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 10: Q.3 (page 694)

The parametric equations $x = 2 \sin t, y = 3 \cos t$ define $a (n)$

Short Answer

Expert verified

$\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$ . This is the standard equation of an Ellipse.

Step by step solution

01

Step 1. description

Given that

$x = 2 \sin t a n d y = 3 \cos t$

Find $a (n)$

02

Step 2. Simplification

$x = 2 \sin t \frac{x}{2} = \sin t \frac{x^{2}}{4} = \sin^{2} t e q n . 1 y = 3 \cos t \frac{y}{3} = \cos t \frac{y^{2}}{9} = \cos^{2} t e q n . 2 e q n . 1 + e q n . 2 \frac{x^{2}}{4} + \frac{y^{2}}{9} = \sin^{2} t + \cos^{2} t \frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

this is the standard form of an ellipse.

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Most popular questions from this chapter

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

$x^{2} = - 4 y$

Find the vertex, focus, and directrix of each parabola. Graph the equation by hand. Verify your graph using a graphing utility.

$x^{2} = 4 y$

1. The formula for the distance d from $P_{1} = (x_{1}, y_{1}) t o P_{2} = (x_{2}, y_{2})$ is d = _____.

In Problems 15鈥�18, the graph of a hyperbola is given. Match each graph to its equation.

Equations:

$(A) \frac{x^{2}}{4} - y^{2} = 1 (B) x^{2} - \frac{y^{2}}{4} = 1 (C) \frac{y^{2}}{4} - x^{2} = 1 (D) y^{2} - \frac{x^{2}}{4} = 1$

Graph:

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.

Focus is at $(- 4, 0)$ and vertex is at $(0, 0)$ .

See all solutions

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