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  • The lines <img alt="\mathrm{3 x-4 y+\lambda=0\: and \: 6 x-8 y+\mu=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B3%20x-4%20y&plus;%5Clambda%3D0%5C%3A%20and%20%5C%3A%206%2

The lines \mathrm{3 x-4 y+\lambda=0\: and \: 6 x-8 y+\mu=0} are tangents to the same circle. The radius of the circle is
 

Option: 1

\mathrm{\left|\frac{2 \lambda-\mu}{20}\right|}

 


Option: 2

\mathrm{\left|\frac{2 \mu-\lambda}{20}\right|}
 


Option: 3

\mathrm{\left|\frac{2 \lambda+\mu}{20}\right|}
 


Option: 4

None of these.
 


Answers (1)

best_answer

Diameter = distance between the parallel lines

\mathrm{=\left|\frac{\lambda}{5}-\frac{\mu}{10}\right|=\left|\frac{2 \lambda-\mu}{10}\right| }

\mathrm{ \Rightarrow \text { Radius }=\left|\frac{2 \lambda-\mu}{20}\right| .}

Hence option 1 is correct.



 

Posted by

Sayak

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