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.

Guest Sep 15, 2019

edited by
Guest
Sep 15, 2019

edited by Guest Sep 15, 2019

edited by Guest Sep 15, 2019

#1**+1 **

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

CPhill Sep 15, 2019