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Parametric Equation of a Circle

The locus of ...

Question

The locus of the curve whose perametric equations are $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$ , where $t$ being a parameter is

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Solution

Given, $x = a (\frac{1 - t^{2}}{1 + t^{2}})$ and $y = \frac{2 a t}{1 + t^{2}}$
$\Rightarrow x^{2} + y^{2} = a^{2} (\frac{(1 - t^{2})^{2} + 4 t^{2}}{(1 + t^{2})^{2}})$
$∴ x^{2} + y^{2} = a^{2}$
Which represents a circle of radius $a units .$

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Parametric Equation of a Circle

Standard XII Mathematics

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