The equation $x^{2} + 9 = 2 y^{2}$ is an example of which of the following curves?

hyperbola

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circle

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ellipse

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parabola

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line

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Solution

The correct option is A hyperbola
Given, $x^{2} + 9 = 2 y^{2}$
$\Rightarrow 2 y^{2} - x^{2} = 9$
$\Rightarrow \frac{y^{2}}{9 / 2} - \frac{x^{2}}{9} = 1$
It is in the form of $\frac{y^{2}}{a^{2}} - \frac{x^{2}}{b^{2}} = 1$ which is the equation of hyperbola.
Therefore, the given equation is a equation of hyperbola.

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\frac{1}{4}

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