Question

7.
Eliminate alpha, if x = r cos alpha, y=r sin alpha​

Answer 1

$\underline { \pink { Eliminating \: \alpha: }$

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

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

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

$\implies x^{2} + y^{2} = r^{2} \: cos^{2} \:\alpha + r^{2}\: sin^{2}\:\alpha$

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

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

By Trigonometric Identity :

$\boxed { \orange { cos^{2}\alpha + sin^{2}\alpha = 1 }}$

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

Therefore.,

$\blue { x^{2} + y^{2} = r^{2}}$

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