how is a conics standard equation derived from an ellipse?

Question

this is for my school project, conics section

Answer 1

Depending on how you dut the cross section of a cone you get the following:

1. If the cross section is parallel with the base of the cone -- you get a circle (a subset of an ellipse).

2. If the cross section is somewhere in between parallel with the base and parallel with the angle formed by the side of the cone, the cross section is an ellipse.

3. If the cross section is parallel with the side of the cone, you get a parabola.

4. If the cross section is perpendicular with the base, you get a hyperbola.

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