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What is the equation of a circle whose center is 4 units above the origin in the coordinate plane and whose radius is 6? A. (x-6)²+y²=16 B. (x-4)²+y2=36 C. x²+(y-4)²=36 D. x²+(y-6)²=16

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Final answer:

The equation of the circle is x² + (y - 4)² = 36, so the correct option is C.

Step-by-step explanation:

The equation of a circle is a mathematical formula that describes the shape and location of a circle.

The standard equation of a circle is given by: (x - h)^2 + (y - k)^2 = r^2

where:

(h, k) is the center of the circle

r is the radius of the circle

The equation of a circle can also be written in general form as:

x^2 + y^2 + 2gx + 2fy + c = 0

where:

g and f are the coefficients of the x and y terms, respectively

c is the constant term

In this case, the center is 4 units above the origin, which means the center is at (0, 4).

The radius is 6 units, so r = 6. Plugging these values into the equation, we get:

(x - 0)^2 + (y - 4)^2 = 62


Simplifying, we have:

x^2 + (y - 4)2 = 36


Therefore, the equation of the circle is x^2 + (y - 4)^2 = 36, here the correct option will be C.

User Djamila
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