Question

if x = a cos^3a, y = b sin^3a, then eliminate a​

Answer 1

Step-by-step explanation:

We have,

$x = a \cos^{3} ( \theta)$ and $y= b\sin^{3} ( \theta)$

Now,

$\implies \frac{x}{a} = \cos^{3} ( \theta) \: \: \: and \: \: \: \frac{y}{b} = \sin^{3} ( \theta)$

$\implies \bigg( \frac{x}{a} \bigg)^{ \frac{1}{3} } = \cos ( \theta) \: \: \: and \: \: \: \bigg( \frac{y}{b} \bigg)^{ \frac{1}{3} } = \sin ( \theta)$

We know,

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

$\implies \bigg \{ \bigg(\frac{y}{b} \bigg)^{ \frac{1}{3} } \bigg\}^{2} + \bigg \{ \bigg(\frac{x}{a} \bigg)^{ \frac{1}{3} } \bigg\}^{2} = 1$

$\implies \bigg(\frac{y}{b} \bigg)^{ \frac{2}{3} } + \bigg(\frac{x}{a} \bigg)^{ \frac{2}{3} } = 1$