First slide

Pair of straight lines

Question

The equation to the pair of lines passing through the point (-2,3) and parallel to the pair of lines $x^{2} + 4 x y + y^{2} = 0$ is

Moderate

A

$x^{2} - 4 x y + y^{2} - 8 x + 2 y - 11 = 0$
B

$x^{2} + 4 x y + y^{2} - 8 x + 2 y - 11 = 0$
C

$x^{2} + 4 x y - y^{2} - 8 x + 2 y - 11 = 0$
D

$x^{2} - 4 x y + y^{2} - 8 x - 2 y - 11 = 0$

Solution

$a = 1, 2 h = 4, b = 1, (x_{1}, y_{1}) = (- 2, 3)$
$a {(x - x_{1})}^{2} + 2 h (x - x_{1}) (y - y_{1}) + b {(y - y_{1})}^{2} = 0$

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