Question 1204201
Find an equation in standard form for the ellipse with center at (5, 8),
horizontal axis of length 10 and passes through the point (6, 4).
<pre>
{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}

{{{drawing(400,3200/7,-2,12,-2,14, arc(5,8,10,2*sqrt(50/3)),
circle(5,8,.1), circle(6,4,.1),circle(5,8,.15), circle(6,4,.15),
grid(1) )}}}

Substitute a=10/2=5.  h=5, k=8, x=6, y=4

{{{(6-5)^2/5^2+(4-8)^2/b^2=1}}}

{{{(1)^2/25^""+(-4)^2/b^2=1}}}

{{{1^""/25^""+16^""/b^2=1}}}

Multiply through by 25b<sup>2</sup>.

{{{b^2+400=25b^2}}}
{{{400=24b^2}}}
{{{400/24=b^2}}}
{{{50/3=b^2}}}
{{{sqrt(50/3)=b}}}

{{{(x-5)^2/5^2+(y-8)^2/(50/3)=1}}}

Edwin</pre>