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  • If the line <img alt="\mathrm{x} \cos \theta+\mathrm{y} \sin \theta=2" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bx%7D%20%5Ccos%20%5Ctheta&plus;%5Cmathrm%7By%7D%20%5Csin%2

If the line \mathrm{x} \cos \theta+\mathrm{y} \sin \theta=2 is the equation of a transverse common tangent to the circles \mathrm{x^{2}+y^{2}=4} and \mathrm{x^{2}+y^{2}-6 \sqrt{3} x-6 y+20=0}, then the value of \mathrm{\theta} is:

Option: 1

5 \pi / 6


Option: 2

2 \pi / 3


Option: 3

\pi / 3


Option: 4

\pi / 6


Answers (1)

best_answer

\quad \mathrm{C}_{1} \mathrm{C}_{2}=\mathrm{r}_{1}+\mathrm{r}_{2}

\mathrm{C}_{1}=(0,0) ; \mathrm{C}_{2}=(3 \sqrt{3}, 3) \: \&\: \mathrm{r}_{1}=2, \mathrm{r}_{2}=4

\Rightarrow \quad circle touch each other externally
equation of common tangent is, \sqrt{3} \mathrm{x}+\mathrm{y}-4=0\quad \ldots(1)


comparing it with \mathrm{x} \cos \theta+\mathrm{y} \sin \theta=2
\theta=\frac{\pi}{6}\

Posted by

vishal kumar

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