How to convert r=7/(5-5costheta) into rectangular form?
#r=7/(5-5costheta)#
1 Answer
That's the sideways parabola
Explanation:
This one is interesting because it just diverges; the minimum of the denominator is zero. It's a conic section; the just diverging I think makes it a parabola. That doesn't matter much, but it does tell us we can get a nice algebraic form without trig functions or square roots.
The best approach is sorta backwards; we use the polar to rectangular substitutions when it seems the other way would be more direct.
So
We see
We have an
Our initial observation was
Now we substitute again.
Technically we've answered the question at this point and we could stop here. But there's still algebra to do, and hopefully a reward at the end: maybe we can show this is actually a parabola.
graph{ x = 1/70 ( 25y^2 - 49 ) [-17.35, 50, -30, 30]}
Yes, that's a parabola, rotated
Check: Alpha eyball