Math, asked by PragyaTbia, 1 year ago

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

Answers

Answered by sprao534
2
Please see the attachment
Attachments:
Answered by hukam0685
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 \\\\<br />

since cos²∅+sin²∅=1

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

is the equation after eliminating θ.
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