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Draw the graph of the relation y^(2)=x^(...

Draw the graph of the relation `y^(2)=x^(2)(1-x)`

Text Solution

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We have `y^(2)=x^(2)(1-x)`
`rArr y=+-xsqrt(1-x)`
Let us first draw the graph of `y=f(x) = xsqrt(1-x)`.
This function is defined if `x le1`
For `0 ltx le1, y gt0` and for `x lt 0, y lt 0`
Also `y=0 rArr x =0,1`
When `x to -infty, y to -infty`
`f^(')(x) = (1.sqrt(1-x)-x/(2sqrt(1-x)))`
`(2-3x)/(2sqrt(1-x))`
`f^(')(x)=0 therefore x=2/3`, which is the point of maxima.
Thus, graph of the function is as shown in the adjacent figure.

To draw the graph of `y=-xsqrt(1-x)`, reflect the graph above the graph in the x-axis. Hence the graph of the relation `y^(2)=x^(2)(1-x)` is as shown in the following figure.
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