If "a" is the x coordinate of P, then "a^2" will be the y coordinate of P
The angle of inclination = arctan (a^2 / a) = θ
And r = √ [ x^2 + y^2 ] = √ [a^2 + a^4 ]
The x coordinate will then become : r cos θ = √ [a^2 + a^4] cos [ arctan (a^2/a) ]
And the y coordinate will become : r sin θ = √ [a^2 + a^4] sin [ arctan (a^2/a) ]
This image might help :
Angle POC in the right triangle POC is the angle of elevation = θ......and OP = the hypotenuse = r
The x coordinate is r cos θ and the y coordinate is r sin θ