(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

Medium

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 the pair of lines given by $(x^2+y^2) \cos^2 \theta = (x \cos \theta + y \sin \theta)^2$ are perpendicular to each other,then $\theta$ is equal to

DifficultAP EAMCET 2012

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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:

DifficultAP EAMCET 2002

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The angle between the pair of straight lines $y^2 \sin^2 \theta - xy \sin^2 \theta + x^2(\cos^2 \theta - 1) = 0$ is

Medium

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The number of values of $a$ for which the pair of lines represented by $3ax^2 + 5xy + (a^2 - 2)y^2 = 0$ are at right angles to each other,is

EasyAP EAMCET 2019

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If the angle between the pair of lines given by the equation $ax^2+4xy+2y^2=0$ is $45^{\circ}$,then the possible values of $a$ are:

MediumTS EAMCET 2024

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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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