Find an equation of an ellipse with center (3,2) a=3c foci (1,2),(5,2)?

Answer 1

Hi,

If the foci are (1,2) and (5,2) then the distance from the center (3,2) is 2 units, so "c" = 2. If "a" = 3"c" then "a" = 3(2) or 6. Therefore a² = 36. To find "b" let a² = b² + c² and fill in values for "a" and "c".

6² = b² + 2²
36 = b² + 4
32 = b²

So the equation of the ellipse is:

(x.-.3)².....(y.-.2)²
---------.-..--------.=.1
...36...........32


I hope that helps!! :-)

Answer 2

c = 2
a = 6
b^2 = 36 - 4 = 31
x^2/36 + y^2/31 = 1