Section 8.5

In fact, all of the equations can be converted into one standard equation.

Example B

Example C This equation describes a parabola, because only one of the variables has an exponent of 2. You can now choose whether to convert this equation to standard form or solve for y. The first choice requires completing the square.

 If you graph two conic sections on the same graph, in how many ways could they intersect?  There are four conic sections: circles, ellipses, parabolas, and hyperbolas. Among the members of your group, investigate the possible numbers of intersection points for all ten pairs of shapes. ◦ For example, an ellipse and a hyperbola could intersect in 0, 1, 2, 3, or 4 points, as shown on the next slide.

 For each pair of conic sections, list the possible numbers of intersection points.

Example D First make a sketch of the two curves. The first equation describes an ellipse with center (1, 0). It has a horizontal scale factor of 4 and a vertical scale factor of 3.

Example D The second equation describes a parabola with vertex (-2, 0) and both scale factors of 3. Looking at your sketch, you can expect to find two intersection points.

Example D

Example E