In rectangular - polar conversion,
r^2=x^2+y^2 , x= r cos theta , y= r sin theta r2=x2+y2,x=rcosθ,y=rsinθ
y= 3 x^2+3 x-y^2y=3x2+3x−y2 or
y^2 + y= 3 x^2+3 xy2+y=3x2+3x or
y(y+1)= 3 x(x+1)y(y+1)=3x(x+1) or
cancelr sin theta (r sin theta +1)= 3 cancelr cos theta( r cos theta+1) or
r sin^2 theta+sin theta = 3 r cos ^2 theta+3 cos theta or
r sin^2 theta-3 r cos ^2 theta=3 cos theta - sin theta or
r (sin^2 theta-3 cos ^2 theta) =3 cos theta - sin theta or
r =(3 cos theta - sin theta)/(sin^2 theta-3 cos ^2 theta)
Polar equation of hyperbola is ,
r =(3 cos theta - sin theta)/(sin^2 theta-3 cos ^2 theta)
graph{y=3 x^2+3 x-y^2 [-10, 10, -5, 5]} [Ans]
