Question

What is the nature of the curve $7y^2=5x$

Answer 1

The equation of the given curve is

$F(x,y)=7y^2-5x=0$

Here $F(x,-y)=7{(-y)}^2-5x=7y^2-5x=0$

$F(-x,y)=7y^2-5(-x)=7y^2+5x\ne F(x,y)$

$F(-x,-y)=7{(-y)}^2-5(-x)=7y^2+5x\ne F(x,y)$

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