Equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of straight lines. Find the separate straight lines.

x+y+1 = 0

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2x+3y+4 = 0

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x+y-1 = 0

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x-3y-4 = 0

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Solution

The correct options are
A
x+y+1 = 0

B
2x+3y+4 = 0

It is given that equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents the pair of straight lines

We can write this equation as quadratic equation in x

We have

$2 x^{2} + (5 y + 6) x + 3 y^{2} + 7 y + 4 = 0$

Roots of the given equation

$X = \frac{- (5 y + 6) \pm \sqrt{(5 y + 6)^{2}} - 4.2 (3 y^{2} + 7 y + 4)}{4}$

$= \frac{- (5 y + 6) \pm \sqrt{25 y^{2} + 60 y + 36 - 24 y^{2} - 56 y - 32}}{4}$

$X = \frac{- (5 y + 6) \pm \sqrt{y^{2} + 4 y + 4}}{4}$

$X = \frac{- (5 y + 6) \pm (y + 2)}{4}$

$X = \frac{- 5 y - 6 + y + 2}{4}, \frac{- 5 y - 6 - y - 2}{4}$

Or 4x = -4y - 4 , 4x + 6y + 8 = 0

X + y + 1 = 0 and 2x + 3y + 4 = 0

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Similar questions

Find the equation of the straight line that has y - intercept 5 and is parallel to the straight line x - 3y = 3

Equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of straight lines. If their point of intersection is (h,k) find the value of h-k.

Find the equations of the pair of lines through the origin which are perpendicular to the lines represented $6 x^{2} - 5 x y + y^{2} = 0$

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Equation 2x2+5xy+3y2+6x+7y+4=0 represents a pair of straight lines. Find the separate straight lines.

Equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of straight lines. Find the separate straight lines.