Convert the rectangle equation x^2-y^2=3 to polar form

Question

Convert the rectangle equation x^2-y^2=3 to polar form

 

Convert the polar equation r-3cosθ=0, to rectangular coorinates. Identify the curve 

Answer 1

Convert the rectangle equation x^2-y^2=3 to polar form

 

(r cosΘ)² - (r sinΘ)² = 3

so r² = 3/(cos²Θ - sin²Θ)

 

Convert the polar equation r-3cosθ=0, to rectangular coordinates. Identify the curve

r-3cosθ=0  Multiply through by r

r² - 3rcosθ = 0

x² + y² - 3x = 0

 

It is a circle.