I need help writing equations for ellipses when I am given information. I am doing a review for a Clep exam and I am completely blanking. Please Help!!!

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I need help writing equations for ellipses when I am given information. I am doing a review for a Clep exam and I am completely blanking. Please Help!!!

Mathematics
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Ok... My first question is this: Write the equation of an ellipse with center (2,1); vertex (7,1) and focus (5,1). I know that this is how I start, knowing the center, but what next: \[\frac{ (x-2)^2 }{ ? } + \frac{ (y-1)^2 }{ ? } = 1\]
Hi @mathmate can you help?
SOMEONE PLEASE HELP ME!!!!!!!
|dw:1439810100002:dw| For an ellipse centred at origin, f=sqrt(a^2-b^2)
OK how to I find a^2 and b^2
And my center is not at the origin btw, but thats ok
Since F is on the x-axis, "a" is the distance of the vertex (along the x-axis) from the centre, so a=(7-2)=5. F is at (5-2)=3 units along the x-axis from the centre, so f=3. B is on the y-axis, at a distance b=sqrt(a^2-f^2) (same as f=sqrt(a^2-b^2)). The ellipse is shown in the diagram. The centre elsewhere is easy to adjust, as you have already done.

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