The point of intersection of lines $x^{2} - 5 x y + 4 y^{2} + x + 2 y + 2 = 0$

(- 2, - 1)

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(2, 1)

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(1, 2)

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(- 1, - 2)

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Solution

The correct option is D $(2, 1)$
Point of intersection for pair of lines $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$ is given by $(\frac{h f - b g}{a b - h^{2}}, \frac{g h - a f}{a b - h^{2}})$
Given equation is $x^{2} - 5 x y + 4 y^{2} + x + 2 y + 2 = 0$ ,then point of intersection is given by $⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ \frac{\frac{- 5}{2} \times 1 - 4 \times \frac{1}{2}}{1 \times 4 - {(\frac{- 5}{2})}^{2}}, \frac{\frac{1}{2} \times \frac{- 5}{2} - 1 \times 1}{1 \times 4 - {(\frac{- 5}{2})}^{2}} ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⟹ (2, 1)$

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