બિંદુ (2, 2) માંથી પસાર થતી સુરેખા એ રેખાઓ sq | vedclass

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Question

Given line is passing through point $(2,2)$

and intersect with $\sqrt{3} x + y =0$ and $\sqrt{3} x - y =0$

I am assuming that $O$ is the origin

Vedclass · Accepted Answer

$y - 2 = 0$

Vedclass · Answer

Given line is passing through point $(2,2)$

and intersect with $\sqrt{3} x + y =0$ and $\sqrt{3} x - y =0$

I am assuming that $O$ is the origin $AB$ so (or such) that the triangle $	riangle AOB$ is equilateral.

Given $\sqrt{3} x+y=0$, slope $=\sqrt{(3)}, \Rightarrow \alpha=	an ^{-1}(\sqrt{3})=60$

similarly

$\sqrt{3} x - y =0, 	ext { slope }=-\sqrt{(} 3), \Rightarrow \beta=	an ^{-1}(-\sqrt{3})=60$ $\Rightarrow \angle BOA =180-60-60=60$

For $	riangle OAB$ to be equilateral, Line $AB$ has to parallel to $x$-axis

Hence, the eq of line $AB$ that passes through $(2,2)$ and parallel to $x$-axis is

$y=2$

$y-2=0$

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