What are the foci of the ellipse? Graph the ellipse.
18x2 + 36y2 = 648
The foci of the ellipse can be found using the equation
c = √(a^2 - b^2)
Where a^2 is the larger number between 18 and 36, and b^2 is the smaller number.
a^2 = 36
b^2 = 18
c = √(36 - 18) = √18 = 3√2
The foci are located at (0, 3√2) and (0, -3√2).
To graph the ellipse, we can rewrite the equation in standard form:
x^2/9 + y^2/18 = 1
This gives us a semi-major axis of 3 (sqrt(9)) and a semi-minor axis of √(18) or 3√2. The center of the ellipse is at (0,0) and the foci are located at (0, 3√2) and (0, -3√2).
The graph of the ellipse is:
In the shape of the graph, the two foci points are shown at (0, 3√2) and (0, -3√2) on the y-axis. The ellipse is symmetrical about the y-axis.