Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex at $(0, 0)$ , axis of symmetry is the x-axis; containing the point $(2, 3)$ .

The equation of a parabola is $y^{2} = \frac{9}{2} x$ . The points are $(\frac{9}{8}, \frac{9}{4})$ and $(\frac{9}{8}, - \frac{9}{4})$ .

The graph of a parabola is :

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given vertex is at the point $(0, 0)$ and the axis of symmetry is the x-axis and containing the point $(2, 3)$ .

Step 2. Equation of a parabola.

The vertex is at the origin, the axis of symmetry is the x-axis and the graph contains a point in the first quadrant. The general form of the equation is

$y^{2} = 4 a x$

Because the point $(2, 3)$ is on the parabola, the coordinates $x = 2, y = 3$ must satisfy the equation of the parabola. Substitute the values, we get

$3^{2} = 4 a (2) 9 = 8 a \Rightarrow a = \frac{9}{8}$ .

The equation will be $y^{2} = \frac{9}{2} x$ .

Step 3. Latus Rectum.

The focus is at the point $(\frac{9}{8}, 0)$ . The two points that determines the latus rectum by letting $x = \frac{9}{8}$ . Then,

$y^{2} = \frac{9}{2} x y^{2} = \frac{9}{2} (\frac{9}{8}) y^{2} = \frac{81}{16} y = \pm \frac{9}{4}$ .

The points are $(\frac{9}{8}, \frac{9}{4})$ and $(\frac{9}{8}, - \frac{9}{4})$ .

Step 4. Graphing Utility.

The graph of a parabola is

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex at $(0, 0)$ , axis of symmetry is the x-axis; containing the point $(2, 3)$ .

Step by Step Solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus Rectum.

Step 4. Graphing Utility.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand. Vertex at 0,0, axis of symmetry is the x-axis; containing the point 2,3.

Step by Step Solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus Rectum.

Step 4. Graphing Utility.

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Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex at $(0, 0)$ , axis of symmetry is the x-axis; containing the point $(2, 3)$ .