Question 1190957


 
given:


Vertex ({{{6}}},{{{3}}})  
foci ({{{-4}}},{{{3}}}) and ({{{4}}},{{{3}}}) =>{{{c}}} is the distance between foci and center=>{{{c=4}}}
and centre is half way between foci: at ({{{0}}},{{{3}}}) ->{{{h=0}}} and {{{k=3}}}

{{{a}}}  is the distance between vertices and center =>{{{a=6}}} 

{{{b^2=6^2-4^2=36-16=20}}}
Standard equation for this ellipse is

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

your equation is:

{{{(x - 0)^2/6^2 + (y - 3)^2 /20= 1}}}

{{{x^2/36 + (y-3) ^2 /20= 1}}}


{{{ drawing(600, 600, -10, 10, -10, 10,
circle(-4,3,.12), locate(-4,3,F(-4,3)),
circle(4,3,.12), locate(4,3,F(4,3)),
circle(6,3,.12), locate(6,3,V(6,3)),
circle(0,3,.12), locate(0,3,C(0,3)),
graph(600, 600, -10, 10, -10, 10,  (1/3)(9 - sqrt(5) sqrt(36 - x^2)), (1/3)(sqrt(5) sqrt(36 - x^2) + 9))) }}}