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Position of a Point W.R.T Hyperbola

The position ...

Question

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

inside

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outside

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lies on

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None of these

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Solution

The correct option is A inside
Given Hyperbola is $9 x^{2} - y^{2} = 1$
and the point is $(2, 5)$
Now $9 (2)^{2} - 5^{2} - 1 = 10 > 0$
Hence the given point lie inside the hyperbola

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Similar questions

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

(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

(5, - 4)

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

(2, 5)

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

(2, 5)

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

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