Math, asked by warsiali946, 16 hours ago

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

Answers

Answered by pulakmath007
2

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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