Posted by Mary on Monday, January 19, 2009 at 7:22am.
5(x^2 + 6x + 9) + 64(y^2 + 2x + 1) -45 -64 -211 = 0
5(x+3)^2 + 64 (y+1)^2 = 320
(x+3)^2/64 + (y+1)^2/5 = 0
Shouldn't the center be at (-3, -1) ?
The semimajor axis length (along the x direction) is a = sqrt64 = 8 and the semiminor axis length is b = sqrt5. The foci are at y = -1, and x = -3 +/- c, where
c^2 = a^2 - b^2 = 64 - 5 = 59
Add and subtract the semimajor axis lengths from the center coordinate to get the vertex locations.
I can't help you with the graphing part. You will need to locate the center on a graph, plot the vertex locations, and compute the coordinates of some intermediate points along the curve.
It is possible that I have made some math errors myself, so check my work.
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