Question

The point $(2,5)$ lies ______________ the hyperbola $81x^2-y^2=1$ is

• A. Inside
• B. Outside
• C. On
• D. None of the above

Answer 1

The correct option is A Inside

If the point $(x_1,y_1)$ lies outside, on or inside the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ then $\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1<,=$ or $>0$.

$S_1=81\ast 4-25-1=298>0$

Point $P$ lies inside