Question

The position of the point $(5,-4)$ relative to the hyperbola $9y^2-x^2=1$ is :

• A. inside
• B. outside
• C. on the hyberbola
• D. on the directrix of hyperbola

Answer 1

The correct option is A inside

Here $S(x,y)=9y^2-x^2-1$
and
$S(5,-4)=9(-4{)}^2-(5{)}^2-1=144-25-1=118>0$
So the point $(5,-4)$ lies inside the hyperbola $9y^2-x^2=1$