Question 1190962

The equation of an ellipse is 

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

where  ({{{h}}},{{{k}}}) is the center, a and b are the lengths of the semi-major and the semi-minor axes.

given: foci ({{{-4}}}, {{{2}}}) and ({{{4}}},{{{2}}}) ->

center is half way between foci: ({{{h}}},{{{k}}})=({{{(-4+4)/2}}},{{{(2+2)/2}}})=({{{0}}},{{{2}}})
=>{{{h=0}}} and {{{k=2}}}

length of major axis is 10=>{{{2a=10}}}->{{{a=5}}}

Thus, {{{a=5}}}, {{{c=4}}}, {{{h=0}}}, and {{{k=2}}}

 then, {{{b=sqrt(5^2-4^2)=sqrt(9)=3}}}

your equation is:

{{{(x-0)^2/5^2+ (y-2)^2/3^2 =1 }}}

{{{x^2/25+ (y-2)^2/9 =1 }}}


{{{ drawing(600, 600, -10, 10, -10, 10,
circle(-4,2,.12), locate(-4,2,F(-4,2)),
circle(4,2,.12), locate(4,2,F(4,2)),
graph(600, 600, -10, 10, -10, 10, (1/5)(10 - 3sqrt(25-x^2)), (1/5)(3sqrt(25 -x^2)+ 10))) }}}