I've had several problems in my homework asking me to find the coefficients for different quadric surfaces using only 2 given points, and a picture to possibly find more points from. For example, I have an image of this elliptic paraboloid:
EDIT: I apparently need more reputation points to post images. Pretend you're looking at a plot of an elliptic paraboloid oriented to grow upward along the z-axis, with the plot running from -4 thru 4 on the x axis, -2 thru 2 on the y axis, and 0 thru 1 on the z axis. Beautiful, isn't it?
I know it has the basic form of $(\frac{x}{a})^2 + (\frac{y}{b})^2 = \frac{z}{c}$, and I know that it exists on the points (2,0,1) and (0,2-1), but I'm not sure what I can do with this information to derive the coefficients?