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