Write the equation of a circle with center (-2, 0) and area = 64 pi

Answer:The required equation in standard form is [tex](x+2)^2+y^2=64[/tex]Step-by-step explanation:The equation of a circle with center (h,k) an radius, r units is given by the formula;[tex](x-h)^2+(y-k)^2=r^2[/tex]The given circle has center (-2,0) and radius squared can be calculated from the given area, which is [tex]64\pi[/tex][tex]\pi r^2=64\pi[/tex][tex]\implies r^2=64[/tex]We substitute these values into the formula to obtain;[tex](x--2)^2+(y-0)^2=64[/tex]We simplify to get;[tex](x+2)^2+y^2=64[/tex]