Convert r = 1 / (6cos(θ)+8sin(θ)) to an equation in rectangular coordinates (i.e., in terms of x and y).

Question

A similar example I found, where r = 1 / (cos (θ) − sin (θ)), found the rectangular equation to be y = x - 1. How would this answer change for my problem now that sin and cos have coefficients?

Answer 1

the coefficients just change the slope of the line.
r(6cosθ+8sinθ) = 1
6x+8y = 1