Question

Eliminate θ from x = a cos⁴ θ; y = b sin⁴ θ

Answer 1

Please see the attachment

Answer 2

Answer:

$\sqrt{\frac{x}{a} }+\sqrt{\frac{y}{b} }=1$

is the equation after eliminating  θ.

Step-by-step explanation:

To Eliminate θ from x = a cos⁴ θ; y = b sin⁴ θ

we must use trigonometric identities

x = a cos⁴ θ

$\frac{x}{a}= cos^{4} \theta$
taking square root both side
$\sqrt{\frac{x}{a} } =cos^{2} \theta$.....eq1

$y=b sin^{4}\:\theta\\\\ \frac{y}{b}= sin^{4}\theta\\\\\sqrt{\frac{y}{b} }=sin^{2} \theta.....eq2$

Add both eq 1 and 2

$\sqrt{\frac{x}{a} }+\sqrt{\frac{y}{b} }=cos^{2} \theta+sin^{2} \theta$

since cos²∅+sin²∅=1

$\sqrt{\frac{x}{a} }+\sqrt{\frac{y}{b} }=1$

is the equation after eliminating θ.