Question

What is the polar form of the equation
3x - 4y = 12?

The answer is r = 12/ (3cosx - 4 sinx)
(x = theta)

I don't know how to get the answer though.

Answer 1

draw a right-angled triangle in the standard position in quadrant I with sides x,y and r and angle Ø

we know sinØ = y/r
so y = rsinØ
similarly
x = rcosØ

so just substitute...
3x - 4y = 12
3rcosØ - 4rsinØ = 12
r(3cosØ - 4sinØ) = 12
r = 12/(3cosØ - 4sinØ)

Answer 2

Wow, I never thought of factoring out the r, heh. Thanks.