Consider the circle with an equation in standard form: (x - 4) ² + (y + 2) ² = 36. Explain in 2-3 sentences or explain the steps used to find the radius and the center.

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Mathematics

13 October, 18:59

Consider the circle with an equation in standard form: (x - 4) ² + (y + 2) ² = 36. Explain in 2-3 sentences or explain the steps used to find the radius and the center.

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Karlee Rangel · Answer 1

The center of this circle is found at (4, - 2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is (x - h) ² + (y - k) ² = r². In this equation, (h, k) is the center of the circle and r is the radius.

From the given equation, (x - 4) ² + (y + 2) ² = 36, h is already subtracted from x, so h = 4, but the k is not subtracted, so (y + 2) = [y - (-2) ], and we see that k is - 2. Therefore, the center of the circle is (4, - 2) and 36 = r². By taking the square root of 36, we find that r = 6.

The center of this circle is found at (4, - 2) and the radius is 6.