Question 1197617

let say the sun is located in focus whose coordinates are ({{{0}}},{{{0}}}), -> ({{{h+c}}},{{{k}}}) and -> ({{{h-c}}},{{{k}}})
 
 two vertices are {{{147}}} and {{{152}}} units away from a particular focus ({{{0}}},{{{0}}}) (so, left and right from origin)

vertices are at ({{{147}}},{{{0}}}) and ({{{-152}}},{{{0}}})-> ({{{h+a}}},{{{k}}}) and ({{{h-a}}},{{{k}}})


 vertices differ {{{5 }}}units, so the other focus will be {{{5}}} units left from origin at  ({{{-5}}}, {{{0}}})

center is half way between: ({{{-5/2}}}, {{{0}}})=({{{-2.5}}}, {{{0}}})

=>{{{h=-2.5}}}, {{{k=0}}}

find {{{a^2}}}:

{{{h+a=147}}}

{{{-2.5+a=147}}}

{{{a=147+2.5=149.5}}}

{{{a^2=22350.25}}}


find {{{c^2}}}:

{{{h+c=-5}}}

{{{-2.5+c=-5}}}

{{{c^2=(-2.5)^2}}}

{{{c^2=6.25}}}


find {{{b^2}}}:

{{{b^2=a^2-c^2}}}

{{{b^2=22350.25-6.25}}}

{{{b^2=22344}}}


your ellipse is:


{{{(x+2.5)^2/22350.25+y^2/22344=1}}}