Fun with Conics Assignment

Geogebra Now let's work with some virtual conics. Use this link here to see a little more clearly what it looks like when a flat two-dimensional surface intersects with a three dimensional cone: httpsgggwwwgeogebra.org[m[gCgBNFVT Here you can change the position and angle of the plane against a stationary cone. The picture on the right is the drawing of the intersection between the two objects. What happens to the shape on the right when you make the angle 0, or the lowest setting you can? Now what do you think will happen when you put the angle up to the highest setting, what type of conic will we see on the right? And now nally, what setting do you think you'd have to change to get a parabola? Make the parabola on Geogebra, then draw both the left side image of the cone and the right side image of parabola here: Reflection State the general equation for each of the four types of conics we discussed in this project (circles, ellipses, parabolas, and hyperboles}. Be sure to include the differences in the formula for each of the conic sections. What do all of these equations have in common and graphed out. what do each of the shapes of each of these equations have in common? What can we conclude about equations with squared variables and their graphs? Now that we've worked with circles and ellipses in a tangible way, how can we describe the shape of an ellipse as a transformation of the shape of a circle