Five points determine a conic

Okay, let's imagine you are playing with stickers. You have five different stickers: a circle, a square, a triangle, a star, and a heart.

Now, if you want to make a special shape using these stickers, you can't just use any five stickers - you have to use specific ones that work together.

In math, we have a similar rule for shapes called conics. A conic is a special shape that can be made by cutting a cone (you might have seen a cone-shaped party hat before).

To make a conic, you need to choose five specific points on the shape. These points will be the corners or edges of the shape, like the corners of a square or the points on a star.

The five points you choose will determine what kind of conic you make. You might make a circle, an oval, a parabola (which looks like a narrow U shape), a hyperbola (which looks like an X shape), or a degenerate conic (which is a straight line or a point).

So, just like with your stickers, you can't just choose any five points to make a conic - you have to choose the specific points that will create the shape you want.