convert each of the following equation from rectangular to polar.It is best to have the equation in the form r=

Question

convert each of the following equation from rectangular to polar.It is best to have the equation in the form r=.

 

1.x=2

 

2.2x-3y=5

 

3.x^2+y^2=10

 

4.x^2-y^2=4

 

5.x^2+(y-1)^2=1

Answer 1

Recall that the conversion is x = r cos θ and  y = r sin θ. Also useful is x² + y² = r².

 

1. x=2

r cos θ= 2

 

 r = 2 sec θ

 

2.2x-3y=5

2r cos θ - 3r sin θ = 5

 

r = 5/(2 cos θ - 3 sin θ)

 

3. x²+y²=10

r² = 10

 

r = √10

 

4. x^2-y^2=4

r² cos² θ - r² sin² θ = 4

 

r² cos 2θ = 4

 

r = 2√(sec 2θ)

 

5. x²+(y-1)²=1

 

x² + y² - 2y = 0

 

r² = 2r sin θ

 

r = 2sin θ