Question 750027: find the equation of the ellipse given center @(0,0) and the major axis parallel to x-axis distance between foci 4/3squareroot of 33, passing through (2,1)
Answer by josgarithmetic(39621)   (Show Source):
You can put this solution on YOUR website! "distance between foci 4/3squareroot of 33"----
That means the foci are (-(2/3)sqrt(33),0) and ((2/3)sqrt(33),0). Use the distance formula to make the expression for the sum of the distances (-(2/3)sqrt(33),0) to (2,1) and ((2/3)sqrt(33),0) to (2,1). That sum will be equal to 2*a, so you will be able to get a value for a.
Next, you find b.
Use the triangle relationship,  . You already know the value for c,
 , and you already just found a.
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