Question 165719
We have to work backwards from given information to find the major axis length (a) using minor axis length (b) and foci (c).
The general equation for an ellipse centered at (h,k) is given by,
{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}
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.
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Foci for an ellipse are located at {{{0+-c}}}
where {{{c^2=a^2-b^2=5^2}}}.
The length of the minor axis is {{{2b=4}}}
{{{b=2}}}
{{{5^2=a^2-2^2}}}
{{{25=a^2-4}}}
{{{a^2=29}}}
{{{a=sqrt(29)}}}
Since the foci are symmetric about the y-axis, the ellipse is centered at (0,0).
The equation then becomes,
{{{x^2/a^2+y^2/b^2=1}}}
{{{x^2/29+y^2/4=1}}}
{{{4x^2+29y^2=116}}}
{{{ graph( 300, 300, -10, 10, -10, 10, sqrt(4(1-x^2/29)), -sqrt(4(1-x^2/29)) )}}}