Fill in the blank(s) to correctly complete each sentence. The circle with center (3, 6) and radius 4 has equation _________.

검증된 단계별 안내

Recall the standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is given by: \[ (x - h)^2 + (y - k)^2 = r^2 \]

Identify the center \((h, k)\) and radius \(r\) from the problem: here, the center is \((3, 6)\) and the radius is \(4\).

Substitute \(h = 3\), \(k = 6\), and \(r = 4\) into the standard form equation: \[ (x - 3)^2 + (y - 6)^2 = 4^2 \]

Simplify the right side by squaring the radius: \[ (x - 3)^2 + (y - 6)^2 = 16 \]

Write the final equation of the circle as: \[ (x - 3)^2 + (y - 6)^2 = 16 \]

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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

Equation of a Circle

The equation of a circle in the coordinate plane is given by (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. This formula represents all points (x, y) that are exactly r units away from the center.

Coordinates of the Center

The center of a circle is a fixed point from which every point on the circle is equidistant. In the equation, the center coordinates (h, k) shift the circle from the origin to the point (3, 6) in this problem.

Radius and Its Role in the Equation

The radius is the distance from the center to any point on the circle. Squaring the radius (r²) in the equation ensures the distance formula is correctly represented, so for radius 4, r² equals 16.