Question

The equation x + y2-4x+2y=b describes a circle.

Part A
Determine the y-coordinate of the center of the circle.
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Answer 1

-1

Step-by-step explanation:

The given equation can be written as

-3x +y^2 +2y +1=b+1

-3x +(y+1)^2=b+1

(-3x-b)+ (y+1)^2=1

This is to be compared with (x-a)^2 + (y-b)^2=c^2

where (a,b) is the center, and c is the radius of the circle.

Thus, we get y=-1, and this is our answer.