in the equation r= 5/(sin theta +2cos theta) the letters r and theta represent polar coordinates. Write the equivalent equation using rectangular coordinates.

Question

Thanks :)

Reiny · Answer

recall:
sinØ = y/r and cosØ = x/r

so:
r= 5/(sin theta +2cos theta)
r = 5/(y/r + 2x/r)
r = 5/((2x+ y)/r)
r = 5r/(2x + y)
1 = 5/(2x+y)
2x + y = 5 <----- a straight line

proof:
http://www.wolframalpha.com/input/?i=polar+plot+r%3D+5%2F(sin+theta+%2B2cos+theta)