What are the foci of the ellipse? Graph the ellipse.18x2 + 36y2 = 648
To find the foci of the ellipse, we first need to put the equation in standard form:
18x^2 + 36y^2 = 648
Divide by 648:
x^2 / 36 + y^2 / 18 = 1
Now we can see that a^2 = 36 and b^2 = 18. To find the foci, we use the formula c^2 = a^2 - b^2:
c^2 = 36 - 18
c^2 = 18
c = √18
c = 3√2
The foci are located at ±(3√2, 0).
To graph the ellipse, we can start by finding the center, which is (0, 0). From there, we can determine the lengths of the major and minor axes. Since a^2=36, a=6 and b^2=18, b=√18=3√2.
The major axis is along the x-axis with length 2a=12, and the minor axis is along the y-axis with length 2b=6√2.
We can now sketch the ellipse with these dimensions, centred at (0, 0) and foci at (±3√2, 0).