Q 28. Find the equation of the parabol... [FREE SOLUTION]

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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 28. (page 643)

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 $(2, 3)$ .

Short Answer

Expert verified

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 :

Step by step solution

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

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

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,

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

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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91影视

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 $(2, 3)$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus Rectum.

Step 4. Graphing Utility.

One App. One Place for Learning.

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91影视

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 point2,3.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Equation of a parabola.

Step 3. Latus Rectum.

Step 4. Graphing Utility.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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 $(2, 3)$ .