Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

문제 108

3장, 문제 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

검증된 단계별 안내

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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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.