The measure of the angle between the lines x^ | vedclass

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Question

(A) The given equation is $x^{2}+2xy \operatorname{cosec} \alpha+y^{2}=0$. Comparing this with the standard form $ax^{2}+2hxy+by^{2}=0$,we get $a=1$,$

Vedclass · Accepted Answer

$\frac{\pi}{2}-\alpha$

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(A) The given equation is $x^{2}+2xy \operatorname{cosec} \alpha+y^{2}=0$. Comparing this with the standard form $ax^{2}+2hxy+by^{2}=0$,we get $a=1$,$h=\operatorname{cosec} \alpha$,and $b=1$. Let $	heta$ be the angle between the lines. The formula for the angle between the lines is $	an 	heta = \left| \frac{2\sqrt{h^{2}-ab}}{a+b} ight|$. Substituting the values,we get $	an 	heta = \left| \frac{2\sqrt{\operatorname{cosec}^{2} \alpha - 1}}{1+1} ight|$. Since $\operatorname{cosec}^{2} \alpha - 1 = \cot^{2} \alpha$,we have $	an 	heta = \left| \frac{2\sqrt{\cot^{2} \alpha}}{2} ight| = |\cot \alpha|$. Thus,$	an 	heta = \cot \alpha = 	an \left( \frac{\pi}{2} - \alpha ight)$. Therefore,$	heta = \frac{\pi}{2} - \alpha$.

The measure of the angle between the lines $x^{2}+2xy \operatorname{cosec} \alpha+y^{2}=0$ is

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