Convert $r^2-5r+6=0$ to a rectangular coordinates

Question

The factor form of that expression is: $(x-2)(x+3)$ but I could be more simpler.

Thanks for a while.

Answer 1

HINT: From $r^2-5r+6-0$ you get $(r-2)(r-3)=0$, and therefore $r=2$ or $r=3$.

• What are the equations in rectangular coordinates for $r=2$ and $r=3$? This is easy if you recognize what geometric shapes are involved.

• Suppose that you get equations $f(x,y)=0$ and $g(x,y)=0$ for the rectangular equations representing $r=2$ and $r=3$. What does the equation $f(x,y)\cdot g(x,y)=0$ represent?