If $2 x^{2} - 10 x y + 26 y^{2} + 5 x - 16 y - 3 = 0$ represents a pair of straight lines, then the point of intersection of those lines is

(2, - 3)

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(5, - 18)

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(- 10, \frac{- 7}{2})

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(- 10, \frac{- 3}{2})

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Solution

The correct option is D $(- 10, \frac{- 7}{2})$
The point of intersection of the pair of straight lines represented by $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ is given by:
$(\frac{h f - b g}{a b - h^{2}}, \frac{g h - a f}{a b - h^{2}})$

Here, $a = 2$ , $b = 13$ , $h = - 5$ , $g = 5 / 2$ , $f = - 8$ and $c = - 3$
$(\frac{h f - b g}{a b - h^{2}}, \frac{g h - a f}{a b - h^{2}}) = (- 10, \frac{- 7}{2})$

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