Answer

Translate each equation into polar coordinates.

• We can square the terms first or replace x and y first. If we square the terms first, we find

Rearranging, and remembering that we can replace x² + y² with r², we find

Since we have r² and r terms, it's not reasonable to isolate r by itself.

• Replace x and y to find

If r≠ 0 then we can divide both sides by r to find

• Square first to find

Then replace:

It's reasonable to separate out r² in this equation. Remember that factoring r² out from r² leaves 1 behind.