The equation of the bisectors of the angles b | vedclass

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Question

(A) The general equation of a pair of lines passing through the origin is $ax^2 + 2hxy + by^2 = 0$.Comparing this with the given equation ${x^2} + 2xy

Vedclass · Accepted Answer

${x^2} - {y^2} = 0$

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(A) The general equation of a pair of lines passing through the origin is $ax^2 + 2hxy + by^2 = 0$.Comparing this with the given equation ${x^2} + 2xy \cot 	heta + {y^2} = 0$,we get $a = 1$,$h = \cot 	heta$,and $b = 1$.The equation of the bisectors of the angles between the lines is given by the formula $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$.Substituting the values,we get $\frac{x^2 - y^2}{1 - 1} = \frac{xy}{\cot 	heta}$.Since the denominator on the left side is $0$,the equation becomes $x^2 - y^2 = 0$.

The equation of the bisectors of the angles between the lines represented by ${x^2} + 2xy \cot \theta + {y^2} = 0$ is

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