Question

Eliminate theta from given equation x=r cos theta, y=r sin theta​

Answer 1

SOLUTION

TO DETERMINE

To eliminate θ from given equation

x = r cos θ , y = r sin θ

FORMULA TO BE IMPLEMENTED

We are aware of the formula that

$\sf{{ \sin}^{2} \theta + { \cos}^{2} \theta = 1}$

EVALUATION

Here it is given that x = r cos θ , y = r sin θ

Now Squaring and adding we get

$\sf{ {x}^{2} + {y}^{2} = {r}^{2} { \cos}^{2} \theta + {r}^{2} { \sin}^{2} \theta }$

$\sf{ \implies {x}^{2} + {y}^{2} = {r}^{2} ( { \cos}^{2} \theta + { \sin}^{2} \theta) }$

$\sf{ \implies {x}^{2} + {y}^{2} = {r}^{2} \times 1 }$

$\sf{ \implies \: {x}^{2} + {y}^{2} = {r}^{2} }$

Which is the required equation

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