Find a polar equation for the curve represented by the given Cartesian equation.

Question

2x+3y=6

 

A) 2sinθ+3cosθ=6r

B) r(2cosθ+3sinθ)=6

C) r(2sinθ+3cosθ)=6

D) 2cosθ+3sinθ=6r

Answer 1

x=rcosθ

y=rsinθ

2x+3y=6

2(rcosθ)+3(rsinθ)=6

r(2cosθ)+r(3sinθ)=6

r(2cosθ+3sinθ)=6 which is B)

 

Answer 2

Since x= rcos theta and

y- r sin theta.

 

We sub in and get 

2rc os theta +3r sin theta= 6

Factroring out the r

r(2 cos theta +3 sin theta)=6

 

So B.