The equation x^2+y^2-4x+2y=b describes a circle. determine the y-coordinate of the center of the circle.
the radius of the circle is 7 units. what is the value of b in the equation?

Step-by-step explanation:

The equation is given as:

Upon solving this equation, we have

which can be written as:

                  (1)

Thus, the y- coordinate of the center of the circle is .

Now, comparing the equation (1) with the equation of circle, we have

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

Thus, on comparing, we have

⇒

Also, it is given that the radius of the circle is 7 units, thus putting r=7 in above equation, we get

⇒

⇒

⇒

Thus, the value of b is 44 units in the given equation.