I'm suppose to convert
r = 2/(4cos θ − 7sin θ) to Cartesian coordinates.
I divided both sides by r and got 1=2/(4x+7y) but it is incorrect. What am I doing wrong?

Question

I'm suppose to convert 
r = 2/(4cos θ − 7sin θ) to Cartesian coordinates. 
I divided both sides by r and got 1=2/(4x+7y) but it is incorrect. What am I doing wrong?

tkhunny · Answer

Why do you believe that to be "wrong"?

Perhaps if you multiplied by $4\cos(\theta) - 7\sin(\theta)$, instead.

tkhunny · Answer

BTW, how did you get -7y rather than +7y?

anonymous · Answer

sorry that was a typo, i had -7y

anonymous · Answer

I got 4x - 7y -2 =0 as my answer now

tkhunny · Answer

Well, we do need to exclude r = 0, but other than that, does someone STILL believe it to be incorrect?

anonymous · Answer

I think it is correct now :)

anonymous · Answer

I only included the 0 because they asked to write it in an equation form.

tkhunny · Answer

No, no.  That was fine all the way.  My point was this...

1) In the original equation x = y = 0 is NOT allowed.
2) In the final form, that exclusion is not apparent.  We have to remember it.

anonymous · Answer

ahhh I understand

anonymous · Answer

You've been helping a lot. I like how you make mee find the answer rather than telling it to me directly.

tkhunny · Answer

Note: There are other restrictions in the original equation.  I'll just show you and you can ponder it when you get bored, sometime.  :-)

$4\cos(x) - 7\sin(x) = \sqrt{65}\cos(x-atan(-7/4)) = 0$

Wherever that thing is zero, beings as it is in the denominator, must be excluded.

anonymous · Answer

that looks interesting, I'll ponder on it for sure.