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Determine the center and radius of the circle with equation (x+3)² + (y − 2)² = 16​

User Rixter
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Answer: Center: (-3, 2). Radius: 4.

Explanation:

The x-coordinate of the center of the circle is given by the constant within the parenthesis with variable x. Whatever number makes the equation x + 3 = 0 is the x-coordinate of the center of the circle, which in this case is -3.

The y-coordinate of the center of the circle is given by the constant within the parenthesis with variable y. Whatever number makes the equation y - 2 = 0 is the y-coordinate of the center of the circle, which in this case is -2.

The radius of the circle is the square root of the constant on the other side of the equation. So, r =
√(16) = 4.

The explanation is from the equation of a circle in a graph:



(x-h)^2 + (y-k)^2 = r^2

h and k in this equation stand for the coordinates of the center of the circle, with h being the x-coordinate and k being the y-coordinate. IN your equation, we have:


(x+3)^2 + (y-2)^2 =16

Which can also be written as


(x-(-3))^2 + (y-(2))^2=16

See the correlation of numbers -3 and 2 with h and k?

Notice also how the equation contains
r^2, so to find the radius you do
√(r^2).

User Khalifa
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