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

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Answer:

  • The coordinates of the point p are:
    (x,xtan\alpha )

Step-by-step explanation:

1. Name the angle of inclination of the line joining p to the origin α.

2. Find the relation between the coordinates of the point (x,y)

When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).

As per the definition of the tangent trigonometric ratio you have:


  • tan\alpha =(y)/(x)

From which you can clear y:


  • y=xtan\alpha =>(x,y)=(x,xtan\alpha )

Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.

User Illes Peter
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