Draw the graph of the relation `(y-x)^(2)=x^(3)`

Explanation

We have `(y-x)^(2)=x^(3)`
We must have `x ge0`
`rArr y-x=+-x^(3//2)`
`rArr y=x+x^(3//2)`………………(i)
or `y=x-x^(3//2)`…………..(ii)
Function (i) is an increasing function and always non-negative. So its graph lies above the x-axis.
Function (ii) meets the x-axis, where `x-x^(3//2)=0` or `x=0,1`
When `x to infty, x - x^(3//2) to -infty`
From these information, we can plot the graph of functions as shown in the following figure.