Question

What is the nature of the curve $x^2-3y^2-7=0$

Answer 1

The equation of the given curve is

$F(x,y)=x^2-3y^2-7=0$

Here $F(x,-y)=x^2-3{(-y)}^2-7=x^2-3y^2-7=0=F(x,y)$

$F(-x,y)={(-x)}^2-3y^2-7=x^2-3y^2-7=0=F(x,y)$

$F(-x,-y)={(-x)}^2-3{(-y)}^2-7=x^2-3y^2-7=0=F(x,y)$

$\therefore$ the given curve is symmetrical about the $x-$axis,$y-$axis and about the origin.