Question

What is the nature of the curve $y^2-7x=0$

Answer 1

The equation of the given curve is

$F(x,y)=y^2-7x=0$

Here $F(x,-y)={(-y)}^2-7x=y^2-7x=0=F(x,y)$

$F(-x,y)=y^2-7(-x)=y^2+7x\ne F(x,y)$

$F(-x,-y)={(-y)}^2-7(-x)=y^2+7x\ne F(x,y)$

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