Change to polar coordinates the equation: $x^{2} + y^{2} = a^{2}$

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Solution

General polar form $(r, θ)$

$r = \sqrt{x^{2} + y^{2}}$
$x = r cos θ$
$y = r sin θ$
$θ = {tan}^{- 1} \frac{y}{x}$

Now given that
$x^{2} + y^{2} = a^{2}$
$\Rightarrow r^{2} = a^{2}$

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