Question

Determine the position of the point (2, - 3) with respect to the hyperbola $\frac{x^2}{9}-\frac{y^2}{25}$.

• A. Inside
• B. outside
• C. on the periphery
• D. None of these

Answer 1

The correct option is B outside

S:$\frac{x^2}{9}-\frac{y^2}{25}-1=0$

$S(2,3)\Rightarrow \frac{4}{9}-\frac{9}{25}-1$

$=\frac{19}{25}-1=\frac{-6}{25}$

$S(2,3)<0$

It lies outside hyperbola