Question 134077
The equation of an ellipse with center at (h,k) and major axis length 2a, minor axis length 2b is:


{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}


Your ellipse:  {{{h=-4}}}, {{{k=-5}}}


Length of major axis:  {{{-1-(-7)=6}}} => {{{a=3}}}


Length of minor axis:  {{{-3-(-7)=4}}} => {{{b=2}}}


Therefore, the desired equation is:


{{{(x-(-4))^2/3^2+(y-(-5))^2/2^2=1}}}


{{{(x+4)^2/9+(y+5)^2/4=1}}}