Question

Transform the given equation xy=a in Polar coordinates.​

Answer 1

SOLUTION

TO DETERMINE

Transform the given equation xy = a in Polar coordinates.

EVALUATION

Here the given equation is xy = a

Let ( r, θ) be the polar coordinates of the point whose cartesian coordinates are (x, y)

Then we have

x = r cos θ and y = r sin θ

Thus we have -

$\sf{xy = a}$

$\sf{ \implies \: r \cos \theta.r \sin \theta= a}$

$\sf{ \implies \: {r}^{2} \sin \theta \cos \theta= a}$

$\sf{ \implies \: {r}^{2} (2\sin \theta \cos \theta)=2 a}$

$\sf{ \implies \: {r}^{2} \sin 2\theta =2 a}$

FINAL ANSWER

Hence the required polar form is

$\sf{ \: {r}^{2} \sin 2\theta =2 a}$

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