91Ó°ÊÓ

given,

$f(x,y)=y^2−x^2$

Then for $c=−3,y^2−x^2=−3\text{that is}{y}^2=x^2−3$

Which is an equation of two hyperbolas with a vertex on the -axis at localid="1649872245591" $x=\sqrt{3},-\sqrt{3}$

For $c=−2,y^2−x^2=−2\text{that is}{y}^2=x^2−2$

Which is an equation of two hyperbolas with a vertex on the -axis at localid="1649872254756" $x=\sqrt{2},-\sqrt{2}$

For $c=−1,y^2−x^2=−1\text{that is}{y}^2=x^2−1$

Which is an equation of two hyperbolas with a vertex on the -axis atlocalid="1649872264402" $x=1,-1$

For $c=0,y^2−x^2=0\text{that is}y=x,y=−x$

Which is the equation of two straight lines passing through the origin.

For $c=1,y^2−x^2=1\text{that is}{y}^2=x^2+1$

Which is an equation of two hyperbolas with a vertex on the -axis at $y=1,-1$

For $c=2,y^2−x^2=2\text{that is}{y}^2=x^2+2$

Which is an equation of two hyperbolas with a vertex on the -axis at $y=\sqrt{2},-\sqrt{2}$

For $c=3,y^2−x^2=3\text{that is}{y}^2=x^2+3$

Which is an equation of two hyperbolas with a vertex on the -axis at $\sqrt{3},-\sqrt{3}$