SOLUTION: Convert the equation given in rectangular form into polar form: 6x-7y=5

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Question 1103123: Convert the equation given in rectangular form into polar form:
6x-7y=5
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
.
In polar coordinates,  x = r%2Acos%28theta%29,  y = r%2Asin%28theta%29.


So, in polar coordinates the given equation takes the form


6%2Ar%2Acos%28theta%29+-+7%2Ar%2Asin%28theta%29 = 5,   or


r%2A%286cos%28theta%29-7%2Asin%28theta%29%29 = 5,   or


r = 5%2F%286cos%28theta%29-7%2Asin%28theta%29%29.



Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


This is pretty straightforward, using the basic rules for converting between polar and rectangular: x = r*cos(t), y = r*sin(t)>

Substitute those polar expressions for x and y, then solve for r:
6x-7y+=+5
6rcos%28t%29-7rsin%28t%29+=+5
r%286cos%28t%29-7sin%28t%29%29+=+5
r+=+5%2F%286cos%28t%29-7sin%28t%29%29

It looks strange, when you first start learning about polar coordinates, because the equation of a straight line in rectangular coordinates is so simple.

But yes, that is what the equation of a straight line looks like in polar coordinates.