$x^{2} - y^{2} + 5 x + 8 y - 4 = 0$ represents

rectangular hyperbola

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ellipse

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hyperbola

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pair of lines

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Solution

The correct option is B hyperbola
Given eqn is
$x^{2} + 5 x - y^{2} + 8 y - 4 = 0$
By making complete square ,we get
$x^{2} + 5 x + (\frac{5}{2})^{2} - (\frac{5}{2})^{2} - (y^{2} - 8 y - 16 + 16) = 4$
$\Rightarrow (x + \frac{5}{2})^{2} - (y - 4^{2}) = 4 + 16 + \frac{25}{4}$
$\Rightarrow \frac{(x + \frac{5}{2})^{2}}{\frac{105}{4}} - \frac{(y - 4)^{2}}{\frac{105}{4}} = 1$ , which is equation of hyperbola of the form
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ where $a^{2} = b^{2} = 105 / 4$

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A

B

A B

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