Question

eliminate alpha, if x=r cos alpha, y= r sin alpha.​

Answer 1

Answer:

$\red { x^{2} + y^{2} } \green {= 1 }$

Step-by-step explanation:

$Given \: x = r cos\alpha \:--(1)$

$y = r sin \alpha \: ---(2)$

$x^{2} + y^{2} = (r cos\alpha)^{2} + (r sin\alpha)^{2}$

$\implies x^{2} + y^{2} = r^{2} cos^{2} \alpha + r^{2} sin^{2} \alpha \\= r^{2} ( cos^{2} \alpha + sin^{2} \alpha ) \\= r^{2} \times 1$

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

Therefore.,

$\red { x^{2} + y^{2} } \green { = 1 }$

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