Question 70073
<pre><font size = 5><b>Convert the rectangular equation y = 5x + 4 to a 
polar equation...thanks

Since sin<font face = "symbol">q</font> = y/r, then y = r·sin<font face = "symbol">q</font>
Since cos<font face = "symbol">q</font> = x/r, then x = r·cos<font face = "symbol">q</font>

So substitute r·sin<font face = "symbol">q</font> for y and r·cos<font face = "symbol">q</font> for x

y = 5x + 4

and get

r·sin<font face = "symbol">q</font> = 5r·cos<font face = "symbol">q</font> + 4

Now solve for r, Get all terms that contain r on the
same side of the equation:

r·sin<font face = "symbol">q</font> - 5r·cos<font face = "symbol">q</font> = 4

Factor out r

r(sin<font face = "symbol">q</font> - 5·cos<font face = "symbol">q</font>) = 4

Divide both sides by the parentheses:

           4
r = ----------------
     sin<font face = "symbol">q</font> - 5·cos<font face = "symbol">q</font>
 
Edwin</pre>