Answer:
Step-by-step explanation:
The equation is given as:
\(x^2+y^2-4x+2y=b\)
Upon solving this equation, we have
\(x^2-4x+4+y^2+2y+1=b+4+1\)
which can be written as:
\((x-2)^2+(y+1)^2=b+5\) (1)
Thus, the y- coordinate of the center of the circle is \(y=-1\).
Now, comparing the equation (1) with the equation of circle, we have
\((x-a)^2+(y-c)^2=r^2\)
where r is the radius of the circle and (a,c) is the center.
Thus, on comparing, we have
⇒\(b+5=r^2\)
Also, it is given that the radius of the circle is 7 units, thus putting r=7 in above equation, we get
⇒\(b+5=(7)^2\)
⇒\(b+5=49\)
⇒\(b=44 units\)
Thus, the value of b is 44 units in the given equation.
