To find the foci of the ellipse, we need to first put the equation into standard form and identify the values of a and b:
18x^2 + 361y^2 = 648
Divide by 648 to get:
(x^2/36) + (y^2/648/361) = 1
a^2 = 36, so a = 6
b^2 = 648/361, so b ≈ 1.622
c^2 = a^2 - b^2 = 36 - 648/361 = 36 - 1.794 = 34.206
c ≈ 5.847
The foci are located at (0, ±c), which gives us:
(0, 5.847) and (0, -5.847)
To graph the ellipse, we can plot the center at (0,0), the semi-major axis of length 6 in the x-direction and the semi-minor axis of length √(648/361) ≈ 1.125 in the y-direction, and then sketch the curve. It should look like a horizontally stretched ellipse centered at the origin.
2. What are the foci of the ellipse? Graph the ellipse. (1 point) 18x ^ 2 + 361 ^ 2 = 648
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