Question 1190961


given: 

Center ({{{3}}},{{{2}}}) ->{{{h=3}}},{{{k=2}}}
foci ({{{3}}}, {{{7}}}) ->  {{{b=7}}}
vertex ({{{3}}},{{{-5}}}) ->{{{c=5}}}

it has the transverse axis as the y-axis and its conjugate axis as the x-axis

The equation of an ellipse is 

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

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


then {{{a^2=7^2-5^2=24}}}

{{{(x-3)^2/24+ (y-2)^2/49 =1}}} 


{{{ drawing(600, 600, -10, 10, -10, 10,
circle(3,2,.12), locate(3,2,C(3,2)),
circle(3,7,.12), locate(3,7,F(3,7)),
circle(3,-5,.12), locate(3,-5,V(3,-5)),
graph(600, 600, -10, 10, -10, 10,( 1/12) (24 - 7sqrt(6) sqrt(-x^2 + 6x + 15)),   (1/12) (7sqrt(6) sqrt(-x^2 + 6x + 15) + 24)  )) }}}