Question

A point P in the first quadrant lies on the parabola y=x^2. Express the coordinates of P as functions of the angle of inclination of the line joining p to the origin.

I honestly don't think my math teacher explained this at all. Please help. Thank you very much.

Answer 1

Pick a point, x,y

P(x,y)=(x,2x^2)

now, tanTheta=2x^2/x=2x

and the distance is the length of the hyp, or r= x/cosTheta

P(r,Theta)=( x/cosTheta, arctan 2x) in polar coordinates.