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Q. 39

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Precalculus Enhanced with Graphing Utilities
Found in: Page 644
Precalculus Enhanced with Graphing Utilities

Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

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Illustration

Short Answer

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

y2=-16x

The vertex is 0,0 ,the focus is 4,0 and directrix is x=a ,x=4 .

The graph of the equation shown below.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. Given information .

Consider the given equation y2=-16x .

Step 2. Analyze the equation .

The standard form of parabola is y2=-4ax

Compare the equation with standard form

.localid="1646816750877" y2=-4axy2=-16x-4a=-16 a=4

Further simplify .

Since a=4 the vertex is 0,0 ,the focus is a,0=4,0 and the directrix is localid="1646988458852" x=4

Step 3. Plot the graph .

The graph of the equation y2=-16x using graphic utility is shown below .

Here V is the vertex , F is the focus and line x=4 represents the directrix of the parabola .

Most popular questions for Math Textbooks

Rutherford’s Experiment In May 1911, Ernest Rutherford published a paper in Philosophical Magazine. In this article, he described the motion of alpha particles as they are shot at a piece of gold foil 0.00004 cm thick. Before conducting this experiment, Rutherford expected that the alpha particles would shoot through the foil just as a bullet would shoot through snow. Instead, a small fraction of the alpha particles bounced off the foil. This led to the conclusion that the nucleus of an atom is dense, while the remainder of the atom is sparse. Only the density of the nucleus could cause the alpha particles to deviate from their path. The figure shows a diagram from Rutherford’s paper that indicates that the deflected alpha particles follow the path of one branch of a hyperbola.

(a) Find an equation of the asymptotes under this scenario.

(b) If the vertex of the path of the alpha particles is 10 cm from the center of the hyperbola, find a model that describes the path of the particle.

In Problems 43–52, identify the graph of each equation without applying a rotation of axes.

9x2+12xy+4y2-x-y=0

The graph of a parabola is given. Match graph to its equation.

and equations are,

A) y2=4x C) y2=-4x E) (y-1)2=4(x-1) G) (y-1)2=-4(x-1)B) x2=4y D) x2=-4y F) (x+1)2=4(y+1) H) (x+1)2=4(y+1)

True or False

The equation 3x2+ Bxy + 12y2 = 10defines a parabola if B=-12.

In Problems 31– 42, rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. Refer to Problems 21–30 for Problems 31– 40.

localid="1647365908255" x2+4xy+y2-3=0

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