Equation for an ellipse

May 2008
87
0
Give the equation for the ellipse with foci at (0, +/-2) and semi-major axis 3.

I find that:

a = 3
b = sqrt(5)
c = +/- 2

Thus by the standard equation of the ellipse:

x^2/a^2 + y^2/b^2 = 1

I get:

x^2/9 + y^2/5 = 1

However, the correct answer is supposed to be:

x^2/5 + y^2/9 = 1

What is wrong with my approach?
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
Give the equation for the ellipse with foci at (0, +/-2) and semi-major axis 3.

I find that:

a = 3
b = sqrt(5)
c = +/- 2

Thus by the standard equation of the ellipse:

x^2/a^2 + y^2/b^2 = 1

I get:

x^2/9 + y^2/5 = 1

However, the correct answer is supposed to be:

x^2/5 + y^2/9 = 1

What is wrong with my approach?
note that the foci and major axis are on the y-axis, not the x-axis.