First slide

Pair of straight lines

Question

If the equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of lines, then the equation of pair of lines parallel to them and passing through the point (0,1) is

Moderate

A

$2 x^{2} + 5 x y + 3 y^{2} - 5 x + 6 y = 0$
B

$2 x^{2} + 5 x y + 3 y^{2} + 5 x - 6 y + 3 = 0$
C

$2 x^{2} + 5 x y + 3 y^{2} - 5 x - 6 y + 3 = 0$
D

$2 x^{2} + 5 x y + 3 y^{2} + 5 x + 6 y + 3 = 0$

Solution

$a = 2, 2 h = 5, b = 3, 2 g = 6, 2 f = 7, c = 4$
$a {(x - x_{1})}^{2} + 2 h (x - x_{1}) (y - y_{1}) + b {(y - y_{1})}^{2} = 0$
$2 x^{2} + 5 x y + 3 y^{2} - 5 x - 6 y + 3 = 0$

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