A plane intersects a cone…?
Think about all the other ways a plane can intersect a cone. Make a sketch of each different shape that can be formed. For each shape, explain in words or with a sketch how the plane must cut the cone to form the shape.
Okay, so I know that if it intersects perpendicular to the base, it’ll form a triangle-ish shape. If it intersects diagonally, wouldn’t it make an oval? And how many other ways can it intersect?
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There are two other ways it can intersect. Think about the plane being parallel to one of the sides of the cone. the plane will intersect only one side of the cone – the top or the bottom – and the intersection will be a U-shaped curve. This is called a parabola.
Now tip that plane a little bit so it intersects the other side of the cone. Now you’ll have two U-shapes. This is called a hyperbola. (If you’re British, that would be ‘an hyperbola’.)
So: circle, ellipse, parabola, hyperbola, and two crossed lines.
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