Given the equation (x-4)^2 + (y+7)^2 = 64. A). What is the Center C?  B). What is the length of the radis r?

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The general equation of a circle is: `(x-h)^2 + (y - k)^2 = r^2`

`(h, k)` represents the center of the circle and `r` represents the radius of the circle.

Therefore, in the equation: `(x-4)^2 + (y+7)^2 = 64`

the center of the circle is (4, -7) and the radius = `sqrt(64) = 8`

Final Answer:  center is `(4, -7)`  and radius is `8.`

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`(x-4)^2 + (y+7)^2 = 64`

The standard equation of a circle is:

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

where (h,k) is the center and r is the radius.

Re-writing the given equation in that exact form, it becomes:

`(x-4)^2 + (y- (-7))^2=8^2`

Therefore, the center of the circle is `(4,-7)` and its radius is 8.

Approved by eNotes Editorial Team

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