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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 2 - Functions and GraphsProblema 108
Capitolo 3, Problema 108

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

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Recall the standard form of the equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
Substitute the given center (-2, 4) into the formula. This means h = -2 and k = 4.
Substitute the given radius r = 6 into the formula. Remember to square the radius, so r^2 = 6^2.
Write the equation by replacing h, k, and r^2 in the standard form: (x - (-2))^2 + (y - 4)^2 = 6^2.
Simplify the equation: (x + 2)^2 + (y - 4)^2 = 36. This is the standard form of the equation of the circle.

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Standard Form of a Circle's Equation

The standard form of a circle's equation is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. This format allows for easy identification of the circle's center and radius, facilitating graphing and analysis.
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Circles in Standard Form

Coordinates of the Center

The center of a circle is represented by the coordinates (h, k). In this case, the center is given as (-2, 4), meaning the circle is centered at the point where x = -2 and y = 4 on the Cartesian plane. Understanding the center's coordinates is crucial for correctly applying them in the standard form equation.
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Graphs & the Rectangular Coordinate System

Radius of a Circle

The radius of a circle is the distance from the center to any point on the circle. It is denoted by r and is a critical component in the standard form equation. In this problem, the radius is given as 6, which means that the circle extends 6 units from the center in all directions.
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Circles in Standard Form
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