Rotating Conics Review

In this section, we learned how to find the equation and sketch the graph of a conic section that is not perfectly vertical or horizontal, but on tilted axes. This picture shows the three basic equations needed in this chapter:


Steps:

First, you must use the top equation to find the angle of rotation of the axes. You then use that angle to simplify the bottom two equations. The ultimate goal is to replace x and y in the original conic's equation with x' and y', or the new x and y that correspond with the new axes.