Question

Trace The Curve = X Power 1/3 + Y Power 1/3 = A Power 1/3

Answer 1

Answer with explanation:

The equation of the curve is:

  $\Rightarrow x^{\frac{1}{3}}+y^{\frac{1}{3}}=a^{\frac{1}{3}}\\\ \text{Cubing both sides}\\\\\Rightarrow x+y+3\times x^{\frac{1}{3}}\times y^{\frac{1}{3}} \times (x^{\frac{1}{3}}+y^{\frac{1}{3}})=a\\\\\Rightarrow x+y+3(xya)^{\frac{1}{3}}=a\\\\x+y-a=-3(xya)^{\frac{1}{3}}\\\\\text{Cubing both sides}}\\\\\Rightarrow (x+y-a)^3+27 x a y=0$

Now, tracing the curve by taking ,distinct values of ,a

Suppose, a=1

Take any of x or y one as Independent variable and other as dependent variable , find different pair of Integral value and plot them on the coordinate plane.Join these points ,you will get the required graph of the above function.