Question 1187453


Equation of the ellipse: {{{ (x-h)^2/a^2+(y-k)^2/b^2=1}}} where {{{h}}} and {{{k}}} are the coordinates of the center,  {{{a}}} is semimajor axis length, and {{{b}}} semiminor axis length

given:
foci ({{{-2}}}, {{{3}}}) and ({{{4}}}, {{{3}}}) 
{{{b=4}}}

the center is midpoint between foci, and its coordinates will be at ({{{(-2+4)/2}}},{{{(3+3)/2}}})= ({{{1}}},{{{3}}})=>{{{h=1}}} and {{{k=3}}}

the distance between the foci is equal to {{{2c}}}
{{{2c=sqrt((-2-4)^2+(3-3)^2)}}}
{{{2c=sqrt(36+0)}}}
{{{2c=sqrt(36)}}}
{{{2c= 6}}}
{{{c= 3}}}

substitute it in equation of elipse

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

{{{ (x-1)^2/a^2+(y-3)^2/16=1}}} .............use {{{c}}}and {{{b}}} to calculate {{{a}}}

{{{c^2=a^2-b^2}}}
{{{a=sqrt(c^2+b^2)}}}
{{{a=sqrt(3^2+4^2)}}}
{{{a=sqrt(25)}}}
{{{a=5}}}

and your equation is:

 {{{(x-1)^2/25+(y-3)^2/16=1}}}