SOLUTION: My friend and I think that the answer to this problem is wrong and we would like a second opinion. There are actually two problems, but I will post it on another seperate page. I

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: My friend and I think that the answer to this problem is wrong and we would like a second opinion. There are actually two problems, but I will post it on another seperate page. I      Log On


   



Question 9377: My friend and I think that the answer to this problem is wrong and we would like a second opinion. There are actually two problems, but I will post it on another seperate page. Its and elipse problem. It reads -
Graph the ellipse and find the foci. Here is the equation - (9x^2)+(4y^2)= 9
Our disagreement is over the coordinates in which the foci are located?
Could you please help us?

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
+9+x%5E2+%2B+4+y%5E2+=+9

Divide both sides by 9:
x%5E2+%2B+%284y%5E2%29%2F9+=+1

Rewrite this as:
%28x%5E2%29%2F1+%2B+%28y%5E2%29%2F%289%2F4%29+=+1

The center of the ellipse is at (0,0), and the radius in the x direction is 1, the radius in the y direction is 3%2F2. Therefore the major axis is in the Y-direction, and the foci will be on the y-axis at (0, c) and (0, -c), where 1%5E2+%2B+c%5E2+=+%283%2F2%29%5E2

Solve for c:
1+%2B+c%5E2+=+9%2F4
c%5E2+=+9%2F4+-+1
c%5E2+=+5%2F4
c+=++%28sqrt%285%29%29%2F2+ or c+=+-+%28sqrt%285%29%29%2F2

Therefore, I have the foci at ( 0, %28sqrt%285%29%29%2F2++) and ( 0,+-%28sqrt%285%29%29%2F2++).

R^2 at SCC