Question 1042880
Let's use the genereal equation of an ellipse,
{{{Cx^2+Dy^2=1}}}
Use each point to get a linear equation,
{{{C(2)^2+D(3)^2=1}}}
1.{{{4C+9D=1}}}
and
{{{C(6)^2+D(1)^2=1}}}
2.{{{36C+D=1}}}
Multiply eq. 2 by 9 and subtract eq. 1 from it,
{{{324C+9D-4C-9D=9-1}}}
{{{320C=8}}}
{{{C=8/320}}}
{{{C=1/40}}}
Then,
{{{4(1/40)+9D=1}}}
{{{1/10+9D=1}}}
{{{9D=1-1/10}}}
{{{9D=9/10}}}
{{{D=1/10}}}
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{{{x^2/40+y^2/10=1}}}
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*[illustration gr1.JPG].