Question 1044355
the equation of the ellipse in standard form is:

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

({{{h}}},{{{k}}}) coordinates of the center
if the center is at ({{{2}}},{{{4}}}), means {{{h=2}}} and {{{k=4}}} and so far you have 
{{{(x-2)^2/a^2+(y-4)^2/b^2=1}}}

if the length of the minor axis is {{{24}}}, and we know that the semi-minor axis is half of the minor axis, so

{{{b=24/2=12}}}

 The points where the major axis touches the ellipse are the "vertices" of the ellipse. The point midway between the two sticks is the "center" of the ellipse, and  if a vertex is at ({{{-11}}},{{{4}}}), center is at ({{{2}}},{{{4}}}), distance from {{{-11}}} to {{{2}}} is {{{13}}}, than 

{{{a=13}}}

substitute {{{a}}} and {{{b}}}

 {{{(x-2)^2/13^2+(y-4)^2/12^2=1}}} -> your answer



{{{drawing( 600, 600, -25, 25, -25, 25,
circle(2,4,.13),locate(2,4,C(2,4)),
circle(-11,4,.13),locate(-11,4,V(-11,4)), 
graph( 600, 600, -25, 25, -25, 25, sqrt(144(1-(x-2)^2/13^2))+4,-sqrt(144(1-(x-2)^2/13^2))+4)) }}}