Answer:
12.
Step-by-step explanation:
The given equation is
[tex]x^2+10x+y^2-4y=71[/tex]
It can be written as
[tex](x^2+10x)+(y^2-4y)=71[/tex]
[tex](x^2+10x+5^2)+(y^2-4y+2^2)=71+5^2+2^2[/tex]
[tex](x+5)^2+(y-2)^2=71+25+4[/tex]
[tex](x+5)^2+(y-2)^2=10^2[/tex] ...(i)
The standard form of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex] ...(ii)
where, (h,k) is center and r is radius.
From (i) and (ii), we get
[tex]h=-5,k=2,r=10[/tex]
The center of circle is (-5,2) and radius is 10. So, the maximum value of y is
[tex]Max(y)=k+r=2+10=12[/tex]
Therefore, the maximum value of y is 12.
