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 is at $(4, - 2)$ and focus is at $(6, - 2)$ .

The equation of a parabola is

${(y + 2)}^{2} = 8 (x - 4)$ .

The points are $(6, 2); (6, - 6)$ .

The graph of an equation is

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given vertex is at $(4, - 2)$ and focus is at $(6, - 2)$ .

Step 2. Equation of a parabola.

The vertex is at $(4, - 2)$ and focus $(6, - 2)$ both lie on the horizontal line $y = - 2$ (the axis of symmetry). The distance a from the vertex to the focus is $a = - 2$ .

The parabola opens to the right. The form of a equation is

${(y - k)}^{2} = - 4 a (x - h)$ .

where $(h, k) = (4, - 2)$ and $a = - 2$ . Therefore, the equation is

${(y + 2)}^{2} = 8 (x - 4)$ .

Step 3. Latus rectum.

The two points that determines the latus rectum by letting $x = 6$ , so that

${(y + 2)}^{2} = 8 (x - 4) {(y + 2)}^{2} = 8 (2) {(y + 2)}^{2} = 16 y + 2 = \pm 4 y + 2 = 4, y + 2 = - 4 y = 2, - 6 .$

The points are $(6, 2)$ and $(6, - 6)$ .

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 is at $(4, - 2)$ and focus is at $(6, - 2)$ .

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 is at 4,-2 and focus is at 6,-2.

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 is at $(4, - 2)$ and focus is at $(6, - 2)$ .