Question

The symmetry in curve $x^3+y^3=3axy$ along

• A. $x-axis$
• B. $y-axis$
• C. $Liney=x$
• D. $Oppositequadrants$

Answer 1

The correct option is C $Liney=x$

To begin with, we determine its symmetries. The equation remains the same if you interchange xx and yy. Interchanging xx and yy is equivalent to swapping the xx and yy axes. So, the curve is symmetric about the line y=xy=x

. It is not symmetric about any other line, nor is it symmetric about the origin or opposite quadrants.

So, the correct option is 'C'.