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Perimeter of a Triangle

Find the locu...

Question

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

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Solution

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

Put in $x = a t^{2}$

$\Rightarrow x = a {(\frac{y}{2 a})}^{2}$

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

$\Rightarrow y^{2} = 4 a x$ is the locus of given point

Locus is parabola

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