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  • The lines <img alt="\mathrm{ x-2 y+5=0 \: and\: 4 x-8 y+15=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20x-2%20y&plus;5%3D0%20%5C%3A%20and%5C%3A%204%20x-8%20y&amp

The lines \mathrm{ x-2 y+5=0 \: and\: 4 x-8 y+15=0} are tangent to the same circle. The radius of the circle is
 

Option: 1

\mathrm{\frac{8}{\sqrt{5}} \: units}

 


Option: 2

\mathrm{\frac{\sqrt{5}}{4}\: units}
 


Option: 3

\mathrm{\frac{4}{\sqrt{5}}\: units}
 


Option: 4

\mathrm{\frac{\sqrt{5}}{8}\: units}


Answers (1)

best_answer

The given lines are parallel.

\Rightarrow Diameter of circle = Distance between these lines

\mathrm{ =\frac{\left|5-\frac{15}{4}\right|}{\sqrt{1^2+2^2}}=\frac{\sqrt{5}}{4} }

\mathrm{\Rightarrow \text { Radius }=\frac{\sqrt{5}}{8} \text { units } }

Hence option 4 is correct.



 

Posted by

sudhir.kumar

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