Question

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!!!

Answer 1

@ganeshie8

Answer 2

@nincompoop

Answer 3

@mathmate

Answer 4

@satellite73

Answer 5

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:
\[\frac{ (x-2)^2 }{ ? } + \frac{ (y-1)^2 }{ ? } = 1\]

Answer 6

@UsukiDoll

Answer 7

Hi @mathmate can you help?

Answer 8

SOMEONE PLEASE HELP ME!!!!!!!

Answer 9

For an ellipse centred at origin, f=sqrt(a^2-b^2)

Answer 10

OK how to I find a^2 and b^2

Answer 11

And my center is not at the origin btw, but thats ok

Answer 12

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.