## The Hooked on Conics Challenge

So you have reviewed completing the square (you will need that for tomorrow) and you have proven the standard form equations of parabolas (which is what you did for homework Tuesday night). Now you will use desmos to make an interactive conic parabola (focus, directrix, and all). First a few notes:

A parabola is the set of all points (x,y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

The midpoint between the focus and the directrix is called the vertex, and the line passing through the focus and the vertex is called the axis of the parabola.

**Definition of Parabola**A parabola is the set of all points (x,y) in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

**Note**The midpoint between the focus and the directrix is called the vertex, and the line passing through the focus and the vertex is called the axis of the parabola.

**Equations and Graphs**(This is a screen shot from your textbook)Using the equations and graphs pictured, I thought it would be more fun to use desmos to recreate the equations above so that you all could see how the focus, vertex, graph, and directrix interact. I did the vertical parabola for you, click on the graph below and then play around with the focus and the sliders to see how the graph interacts. Can you make the parabola open downwards? What has to change to make that happen? (If the graph doesn't load below click on this link)

**Your job is to make an interactive

Conic Problems

Conic Problems Answers *Check this after you have made your predictions, or if you are stuck...

__horizontal parabola__. After you have made the second interactive graph you will be able to do the following problems.**Conic Problems

Conic Problems Answers *Check this after you have made your predictions, or if you are stuck...