Question

For \(x=a\cos^3\theta\) and \(y=a\sin^3\theta\), which equation do these parametric equations represent?

विकल्प

• \(x^2+y^2=a^2\)

• \(x+y=a\)

• \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}\)

• \(x^{\frac{3}{2}}+y^{\frac{3}{2}}=a^{\frac{3}{2}}\)

Answer 1

Using the parametric expressions gives \((a\cos^3\theta)^{\frac{2}{3}}+(a\sin^3\theta)^{\frac{2}{3}}=a^{\frac{2}{3}}(\cos^2\theta+\sin^2\theta)\). Since \(\cos^2\theta+\sin^2\theta=1\), the equation is \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}\).