Question

x+2y=3. Rewrite it in polar form as r=f(θ) for some function f. (Hint: Substitute x and y for their polar expressions, and then solve for r ).

Answer 1

To rewrite the equation x+2y=3 in polar form as r=f(θ), we substitute x and y with their polar expressions and solve for r.

Step-by-step explanation:

To rewrite the equation x+2y=3 in polar form as r=f(θ), we substitute x and y with their polar expressions.

Using the relations x=r*cos(θ) and y=r*sin(θ), we can rewrite the equation as r*cos(θ)+2r*sin(θ)=3.

Factoring out r, we get r*(cos(θ)+2*sin(θ))=3. Therefore, the polar form of the equation is r=3/(cos(θ)+2*sin(θ)).