Ellipse Equations Part 1

Expanding these equations builds on a number of skills students already possess. They can expand a binomial and are familiar with clearing denominators through multiplication. The conversion of an ellipse is just a combination of these skills.

Rewriting the numerators is quick, no problems there. We recognize there are denominators, but we’re trying to clear them. But how do you clear two different denominators? How does that manipulate the other terms? Students might observe that this action seems to make the denominators “switch” positions. The remaining distribution and combination of constants is familiar. Generally there are limited struggles. Developing our pattern for binomial expansion was certainly useful, and will later prove to be even more useful as we attempt to unwrap this equation later. Though students are never told they are required to memorize this pattern, if they would like to distribute and combine terms, they are free to do so.

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