Guys, right now I'm learning about conics and about the formula for graphing them. But I'm confused, for the reason outlined: First of all, which axis is semi-minor (m for reference) and which is semi-major (M for reference) doesn't seem to matter to where in the formula for graphing conics it is placed. All that matters is which axis is on the x axis and which is on the y axis. That leads me to wonder what would happen if the ellipse is oriented such that m and M are not on the x axis or y axis. How do we figure it out, then? If we rotate it to figure it out, which axis do we choose to be on the x axis and which on the y? Or does it not matter at all?
EDIT: And in fact, how would we even rotate it? All we'll know is m and M. What would be the formula for the graphing of such a ellipse? Can you even graph it, or does it have to be positioned with m and M on the established axes?
