Question

Express the equation x^2+y^2-6y in polarcoordinates

Answer 1

Understanding these relationships are critical to better understanding how to solve these types of problems.

x=rcos(θ)

y=rsin(θ)

yx=tan(θ)

tan1(yx)=θ

x2+y2=r2

To solve this type of problem one of the first things to look for is a way to make substitutions.

x2+y2=7y

Substitute in r2 for x2+y2

r2=7y

Substitute in rsin(θ) for y

r2=7rsin(θ)

r2r=7rsin(θ)r

r=7sin(θ)→ is the polar form of →x2+y2=7y