Question

What is the nature of the curve $2y^2-5x=0$

Answer 1

The equation of the given curve is

$F(x,y)=2y^2-5x=0$

Here $F(x,-y)=2{(-y)}^2-5x=2y^2-5x=0=F(x,y)$

$F(-x,y)=2y^2-5(-x)=2y^2+5x\ne F(x,y)$

$F(-x,-y)=2{(-y)}^2-5(-x)=2y^2+5x\ne F(x,y)$

$\therefore$ the given curve is symmetrical about the $x-$axis but neither about $y-$axis nor about the origin.