## anonymous one year ago 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!!!

1. anonymous

@ganeshie8

2. anonymous

@nincompoop

3. anonymous

@mathmate

4. anonymous

@satellite73

5. anonymous

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

6. anonymous

@UsukiDoll

7. anonymous

Hi @mathmate can you help?

8. anonymous

9. mathmate

|dw:1439810100002:dw| For an ellipse centred at origin, f=sqrt(a^2-b^2)

10. anonymous

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

11. anonymous

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

12. mathmate

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.