(B) The given equation is of the form $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0

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(B) The given equation is of the form $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing this with $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$,we get $a = 1$,$h = \sqrt{3}$,and $b = 3$.The condition for the lines to be parallel is $h^2 - ab = 0$.Substituting the values,we get $(\sqrt{3})^2 - (1)(3) = 3 - 3 = 0$.Since $h^2 - ab = 0$,the lines represented by the equation are parallel.

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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The lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ are

A
Perpendicular to each other
B
Parallel
C
Inclined at $45^{\circ}$ to each other
D
None of these

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Pair of straight lines

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Angle between the pair of straight lines, Condition for parallel and perpendicular lines

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

EasyTS EAMCET 2011

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If the angle $2 \theta$ is acute,then the acute angle between the pair of straight lines $x^2(\cos \theta - \sin \theta) + 2xy \cos \theta + y^2(\cos \theta + \sin \theta) = 0$ is:

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The angle between the lines represented by the equation $4x^2 - 24xy + 11y^2 = 0$ is given by:

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The angle between the pair of straight lines $x^2 + 4y^2 - 7xy = 0$ is

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The angle between the pair of lines represented by $x^2 + 2xy - y^2 = 0$ is:

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The lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ are

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If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

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