Question

A point P in the first quadrant lies on the graph of the function `f(x) = sqrt x`, how do you express the coordinates of P as function of the slope of the line joining P to the origin?

Answer 1

If m is the slope of line joining the origin O and P (x, `sqrt x)`, the the coordinates of P become `(m^2, m), m >=0`. This is a parametric form of the coordinates, for the curve `y = sqrt x`..

Explanation:

Here, `x >= 0`. The point P is `( x, sqrt x )`.

If m is slope of the line joining the origin `O (0, 0) and P (x, sqrt x ),`
`m = sqrt x / x =sqrt x`.

Now, if m is used as a parameter, P is `(m^2, m), m>=0`.

Thanks to Abhishek Dogra, I have now revised my answer to

remove the error pointed out by him.

The graph is a semi-parabola.

The other half is given by `y = - sqrt x`.