Barrons AP Calculus - David Bock

For the hyperbola, c^2 = a^2 + b^2 , and eccentricity which is greater than 1.

POLAR COORDINATES

RELATIONS WITH RECTANGULAR COORDINATES

53. x = r cos θ;
    y = r sin θ;
    r^2 = x^2 + y^2 ;

SOME POLAR EQUATIONS

54. 
    

    r = a circle, center at pole, radius a.

    
    


55. 
    

    r = 2a cos θ circle, center at (a, 0), radius a.

    
    


56. 
    

    r = 2a sin θ circle, center at (0, a), radius a.

    
    


57. 
    


58. 
    

roses (four leaves)

59. r = cos 2θ.


60. r = sin 2θ.