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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.

 Sep 15, 2019
edited by Guest  Sep 15, 2019
edited by Guest  Sep 15, 2019
 #1
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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

 

 

 

 

 

cool cool cool

 Sep 15, 2019
edited by CPhill  Sep 15, 2019
edited by CPhill  Sep 15, 2019

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