PARAMETER AND PARAMETRIC EQUATION [2]

# PARAMETER AND PARAMETRIC EQUATION [2]

C
10 million points

Obtain parametric equations for the locus $y^2=x^3-x^2$.

PARAMETER AND
chegendungu

C
10 million points

Put $y=t$x in the equation $y^2=x^3-x^2$, then

$t^2x^2=x^3-x^2$

$\therefore t^2=x-1$

$\therefore x=t^2+1$

Therefore the locus may be represented by the parametric equations $x=t^2+1$, $y=t^3+t$

$Note:$ This method is not suitable for all equations, but it works well when the terms are of degree $n$ and $n-1$

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