Textbook Question
Add or subtract, as indicated. See Example 4. (1/a)+(b/a²)
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 51
In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (0, 0), radius 6
Verified step by step guidance1
Identify the general form of the equation of a circle with center at \((h, k)\) and radius \(r\), which is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Since the center is \((0, 0)\), substitute \(h = 0\) and \(k = 0\) into the formula, simplifying it to:
\[ x^2 + y^2 = r^2 \]
Given the radius \(r = 6\), substitute this value into the equation:
\[ x^2 + y^2 = 6^2 \]
Simplify the right side of the equation to express the center-radius form:
\[ x^2 + y^2 = 36 \]
For graphing, plot the center at the origin \((0, 0)\) and draw a circle with radius 6 units extending equally in all directions from the center.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equation of a Circle in Center-Radius Form
The center-radius form of a circle's equation is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. This form directly shows the circle's location and size, making it easier to graph and analyze.
Recommended video:
06:03
Equations of Circles & Ellipses
Identifying the Center and Radius
To write the equation of a circle, you must know its center coordinates (h, k) and radius r. For a circle centered at (0, 0) with radius 6, the equation simplifies to x^2 + y^2 = 36, since h and k are zero and r^2 = 36.
Recommended video:
06:11Introduction to the Unit Circle
Graphing a Circle
Graphing a circle involves plotting its center point and drawing all points at a distance equal to the radius from the center. For a circle centered at the origin with radius 6, plot (0,0) and mark points 6 units away in all directions to sketch the circle.
Recommended video:
06:11Introduction to the Unit Circle
Related Practice
Textbook Question
Find each product. See Example 5. (4x² - 5y) (4x² + 5y)
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Textbook Question
Give (a) the additive inverse and (b) the absolute value of each number. 0.16
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Textbook Question
Determine whether each function is even, odd, or neither. See Example 5. ƒ(x) = 0.5x⁴ - 2x² + 6
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Textbook Question
Add or subtract, as indicated. See Example 4. (1/6m) + (2/5m) + (4/m)
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Textbook Question
Find each product. See Example 5. (4m + 2n)²
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