The second degree equation $x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0$ represents a pair of lines.

True

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False

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Solution

The correct option is A
True

if any second degree equation $a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0$ represents a pair of lines, then

$a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2} = 0$

Now, comparing given equation

$x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0$ with standard second degree equation.

We get,a=1,h= $\frac{3}{2}, b = 2, g = \frac{- 1}{2}, f = 2, c = - 6$

$a b c + 2 f g h - a f^{2} - b g^{2} - c h^{2}$

= $- 12 + 3 - 4 - \frac{1}{2} + \frac{27}{2} = 0$

So,we can say that the equation $x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0$ represents the pair of lines

Given statement is true

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The second degree equation x2+3xy+2y2−x−4y−6=0 represents a pair of lines.

The second degree equation $x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0$ represents a pair of lines.