(a) Prove that the evolute of the curve $x=a \cos ^{3} \theta$ and $y=a \sin ^{3} \theta$ is $(x+y)^{2 / 3}+(x-y)^{2 / 3}=2 a^{2 / 3}$.

Explanation

The given problem is to find the equation of the evolute of the curve x = a cos^3 θ and y = a sin^3 θ. We used the formula for the equation of the evolute and substituted the values of x and y. We then simplified the expression to get the equation of the evolute.

(a) Prove that the evolute of the curve $x=a \cos ^{3} \theta$ and $y=a \sin ^{3} \theta$ is $(x+y)^{2 / 3}+(x-y)^{2 / 3}=2 a^{2 / 3}$.

Explanation

⬆ Related Topic

📘 Syllabus

📝 Practice Questions

🤖 Practice with AI

📚 Related Concepts