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The graph of
\(r = -\frac{5}{2 \cos \theta + \sin \theta}\)
is a line. Find the y-intercept of this line.

 Dec 1, 2018
 #3
avatar+101871 
+1

r = √ [ x^2 + r^2]         

cos θ   = x / r = x /  √ [ x^2 + r^2]  

sin θ =  y / r =    y /  √ [ x^2 + r^2] 

 

So we have

 

√ [ x^2 + r^2]  =      -5

                          ___________________

                          ( 2x + y )  / √ [ x^2 + r^2]

 

 

√ [ x^2 + r^2]  =  -5 √ [ x^2 + r^2] 

                          ______________

                             2x +  y

 

1  =    - 5

         ______

          2x + y

 

2x + y  =  - 5

 

y = -2x + -5

 

 

The y intercept is  -5

 

CORRECTED !!!!

 

 

cool cool cool

 Dec 1, 2018
edited by CPhill  Dec 1, 2018
 #6
avatar+101871 
0

Ah.....just a slight typo....I have mixed up sin and cos in the original denominator....see my corrected answer!!!

 

 

cool cool cool

CPhill  Dec 1, 2018
edited by CPhill  Dec 1, 2018

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