Question

What is the nature of the curve $5x^2+7y=0$

Answer 1

The equation of the given curve is

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

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

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

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

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