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Perimeter of a Triangle

Find the locu...

Question

Find the locus of a point whose co-ordinates are given by $x = a t^{2}, y = 2$ at, where 't' is a parameter.

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Solution

$x = a t^{2}, y = 2 a t$

$y = 2 a t$

$\Rightarrow t = \frac{y}{2 a}$

Put in $x = a t^{2}$ , the value of t

So $x = a . \frac{y^{2}}{4 a^{2}}$

$\Rightarrow y^{2} = 4 a x$

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