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 (2, 0), radius 6

검증된 단계별 안내

Recall that the center-radius form of a circle's equation is given by \[(x - h)^2 + (y - k)^2 = r^2\] where \[(h, k)\] is the center and \[r\] is the radius.

Identify the center coordinates and radius from the problem: the center is \[(2, 0)\] and the radius is \[6\].

Substitute the center coordinates into the formula: replace \[h\] with \[2\] and \[k\] with \[0\], so the equation becomes \[(x - 2)^2 + (y - 0)^2 = r^2\].

Substitute the radius value into the equation: replace \[r\] with \[6\], so the equation becomes \[(x - 2)^2 + y^2 = 6^2\].

Simplify the right side by squaring the radius: the equation is \[(x - 2)^2 + y^2 = 36\]. This is the center-radius form of the circle's equation.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

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

Equation of a Circle in Center-Radius Form

The center-radius form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. This form directly shows the circle's location and size, making it easy to write the equation when the center and radius are known.

Coordinate Geometry and Plotting Points

Understanding how to plot points on the Cartesian plane is essential for graphing the circle. The center (h, k) is the reference point, and the radius determines the distance from the center to any point on the circle, guiding the drawing of the circle's boundary.

Radius and Distance in the Plane

The radius is the fixed distance from the center to any point on the circle. Knowing how to interpret and use this distance helps in both writing the equation and graphing the circle accurately, ensuring all points satisfy the distance condition.

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 (2, 0), radius 6