If necessary, rewrite the equation. Then identify whether the ellipse is vertical or horizontal.
Center: (0,0) Foci: (0,3sqrt(3)) and (0,- 3sqrt(3)) Length of the Major Axis: 12 units Length of the Minor Axis: 6 units Graph:
Practice makes perfect
First, we need to rewrite this equation such that it fits the general equation of an ellipse.
Horizontal Ellipse: & (x- h)^2/a^2 + (y- k)^2/b^2 = 1 [0.8em]
Vertical Ellipse: & (y- k)^2/a^2 + (x- h)^2/b^2 = 1
Because the denominator of the y-variable is greater than the denominator of the x-variable, the equation represents a verticalellipse. Let's rewrite the equation a bit to make it easier to identify the values of h, k, a, and b.
Now we can add and subtract c to find the foci.
Foci
(0,0± 3sqrt(3) )
⇓
(0,3sqrt(3)) and (0,- 3sqrt(3))
We will now use the information we have found to draw the ellipse.
