Question

Transforms 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}xy=a

\sf{ \implies \: r \cos \theta.r \sin \theta= a}⟹rcosθ.rsinθ=a

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

2

sinθcosθ=a

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

2

(2sinθcosθ)=2a

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

2

sin2θ=2a

FINAL ANSWER

Hence the required polar form is

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

2

sin2θ=2a

━━━━━━━━━━━━━━━━