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Convert the polar equation r=3cos(Theta)

 Dec 15, 2014

Best Answer 

 #1
avatar+98173 
+5

r=3cos(Theta)  ...... and to convert to Cartesian form, we have

√(x^2 + y^2)  = 3 (x)/√(x^2 + y^2)    simplify

(x^2 + y^2)  = 3x  subtract 3x from both sides

x^2 - 3x + y^2 = 0  complete the square on x

x^2 - 3x + 9/4 + y^2  = 9/4      factor

(x - 3/2)^2 + y^2  = 9/4

Here is a graph of both forms......https://www.desmos.com/calculator/xty6odyy4z

(Notice that they are the very same graph !!!!)

 

 Dec 15, 2014
 #1
avatar+98173 
+5
Best Answer

r=3cos(Theta)  ...... and to convert to Cartesian form, we have

√(x^2 + y^2)  = 3 (x)/√(x^2 + y^2)    simplify

(x^2 + y^2)  = 3x  subtract 3x from both sides

x^2 - 3x + y^2 = 0  complete the square on x

x^2 - 3x + 9/4 + y^2  = 9/4      factor

(x - 3/2)^2 + y^2  = 9/4

Here is a graph of both forms......https://www.desmos.com/calculator/xty6odyy4z

(Notice that they are the very same graph !!!!)

 

CPhill Dec 15, 2014

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