Answer:
- The coordinates of the point p are: [tex](x,xtan\alpha )[/tex]
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:
- [tex]tan\alpha =\frac{y}{x}[/tex]
From which you can clear y:
- [tex]y=xtan\alpha =>(x,y)=(x,xtan\alpha )[/tex]
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.
