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

Inside

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Outside

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lie on

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None of these

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Solution

The correct option is A
Inside

Simply substitute the point (2, 5) on the LHS of the standard hyperbola,

$9 x^{2} - y^{2} = {9.2}^{2} - 5^{2}$

=9.4-25

=11

$> 1$

This implies that the point lies inside the given hyperbola.

Hence option (a)

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Similar questions

Find the position of the point (5,-4) relative to the
hyperbola $9 x^{2} - y^{2} = 1$

(5, - 4)

9 y^{2} - x^{2} = 1

(5, - 4)

9 y^{2} - x^{2} = 1

9 x^{2} - y^{2} = 1

(7, - 3)

9 x^{2} - 4 y^{2} = 36

(x_{1}, y_{1})

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

\frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1 > 0

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