Question 1045442
 the equation {{{(x^2/640000)+(y^2/630000) = 1}}}


Solution: 

The ellipse has center at the {{{origin}}}, and {{{major}}} axis on the x-axis.

if you compare  {{{(x^2/640000)+(y^2/630000) = 1}}} to  {{{(x^2/a^2)+(y^2/b^2) = 1}}}, you see that

{{{ a^2 = 640000}}}, then {{{a = 800}}}, so the vertices are {{{V[1]}}} is at ({{{-800}}}, {{{0}}}) and {{{V[2]}}} is at({{{800}}}, {{{0}}}). 

Since {{{ a^2 = 640000}}} and {{{b^2 = 630000}}}, then 

{{{c =sqrt(a^2-b^2) }}}
 {{{c =sqrt(640000-630000) }}}
 {{{c =sqrt(10000)}}} 
{{{c=100}}}

Suppose the star is at the focus at the right of the origin (this choice is arbitrary, since we could have chosen instead the focus on the left). Its location is then {{{F}}}({{{100}}},{{{ 0}}}). 
The {{{closest}}} distance is then {{{V[2]F = 700}}} (million kilometers) and the {{{farthest}}} distance is {{{V[1]F = 900}}} (million kilometers).

Answer: 
{{{700}}} million km,the {{{closest}}} distance
and  
{{{900}}} million km, the {{{farthest}}} distance