Question 1204201
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We can't tell with the given information whether the horizontal axis is the major or minor axis.  We can assume it is the major axis and then adjust our results if it turns out that it is the minor axis.<br>
The standard form with center at (5,8) and horizontal major axis of length 10 is<br>
{{{(x-5)^2/5^2+(y-8)^2/b^2=1}}}<br>
Find b^2 using the given point (6,4) on the ellipse.<br>
{{{(6-5)^2/5^2+(4-8)^2/b^2=1}}}
{{{1/25+16/b^2=1}}}
{{{16/b^2=24/25}}}
{{{24b^2=400}}}
{{{b^2=400/24=50/3}}}<br>
Note that b^2=50/3 is less than a^2=25, so the horizontal axis is indeed the major axis.<br>
The standard form of the equation of the ellipse is<br>
ANSWER: {{{(x-5)^2/25+(y-8)^2/(50/3)=1}}}<br>