Question

Convierta la siguiente ecuación rectangular a su forma polar (x^2+y^2)=9(x^2-y^2)

Answer 1

x=r.cos©. y=r.sen©

x^2= r^2.cos^2©

y^2 = r^2.sen^2©=r^2(1-cos^2©)

x^2+y^2 =r^2(cos^2©+sen^2©)=r^2(1)=r^2

==>

r^2=9[r^2.cos^2©-(r^2-r^2.cos^2©)]

r^2=9.r^2(cos^2©-1+cos^2©)

eliminar r^2:

1=9(2.cos^2©-1)

==>

1=18.cos^2©-9

10=18.cos^2©

cos^2©=5/9

√(cos^2©)=√(5/9)

cos©=√5/3