x²+y²+y = 0
For all problems changing between rectangular and polar form,
you should draw this right triangle:
to replace all x's and y's by r's and q's. Also when you see "x²+y²"
you can immediately replace the TWO terms by the ONE term r².
So from that triangle and the Pythagorean theorem, you can easily see
that x²+y² = r², so substituting the ONE TERM r² for the first TWO
terms, you have
r²+y = 0
Then you see from that right triangle that y/r = sin(q) and y = r∙sin(q).
So the final polar equation is
r²+r∙sin(q) = 0
Now to solve that for r:
r²+r∙sin(q) = 0
r[r+sin(q)] = 0
r=0; r+sin(q) = 0
r = -sin(q)
We can ignore r=0 which is the equation of the origin, but since
the circle goes through the origin. So the answer is the polar
equation:
r = -sin(q
Edwin
