# Conic Sections

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Conic sections are shapes that are made when a flat plane (like a sheet of paper) intersects a cone (like an ice cream cone). The intersection can create four different shapes: circles, ellipses, parabolas, and hyperbolas.

A circle is a round shape where all points on the edge (called the circumference) are the same distance from the center. Imagine drawing a big round cookie with a compass - that's a circle!

An ellipse is a shape that is like a stretched-out circle. It has two points called the foci (pronounced foe-sigh) that are inside the shape. If you draw a line from one focus to any point on the edge of the ellipse, and then draw a line from that point to the other focus, the two lines will be the same length. You might have seen ellipses on racetracks - they are often used to mark the start and finish lines.

A parabola is a shape that looks like a smiley face or a frown. It has one focus, and all the points on the parabola are the same distance from the focus as they are from a straight line called the directrix. You can make a parabola by cutting a cone with a plane that is parallel to one side of the cone.

A hyperbola is a shape that looks like two parabolas facing each other. It has two foci, and the difference in distances from any point on the edge to the two foci is constant. You might see hyperbolas in math or science textbooks - they are often used to show how light moves through lenses.

So, conic sections are just four different shapes that you can make by cutting a cone with a flat plane. Pretty cool, huh?