Step 1: Write out the formula
Given the equation of a circle with center (h,k) and radius r, if it is shifted left by a unit and up by b unit, then the function would become
[tex](x-h+a)^2+(y-k-b)^2=r^2[/tex]Step 2: Write out the given value and substitute them into the formula
In this case,
[tex]h=3,k=-8,a=5,b=2,r=5[/tex]Therefore the new equation is given by
[tex]\begin{gathered} (x-3+5)^2+(y-(-8)-2)^2=5^2 \\ (x+2)^2+(y+8-2)^2=5^2 \\ (x+2)^2+(y+6)^2=25 \end{gathered}[/tex]Hence, the new equation for the circle is (x+2)²+(y+6)²=25
