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The lines \mathrm{3x-4y+4=0} and \mathrm{6x-8y-7=0} are tangents to the same circle. The radius of the circle is 

Option: 1

\frac{1}{2}


Option: 2

\frac{3}{4}


Option: 3

\frac{3}{2}


Option: 4

none of these


Answers (1)

best_answer

First tangent line is \mathrm{T_1: 3 x-4 y+4=0}.......(i)

Second tangent line is \mathrm{6 x-8 y-7=0}

or \mathrm{ T_2: 3 x-4 y-\frac{7}{2}=0 }.............(ii)   

Evidently (i) is parallel to (ii). Distance between (i) and (ii) is the length of diameter

\mathrm{ \Rightarrow \quad 2 r=\left|\frac{4-(-7 / 2)}{\sqrt{3^2+4^2}}\right| }

\mathrm{ \Rightarrow 2 r=\left|\frac{15 / 2}{5}\right|=\frac{3}{2} }

\mathrm{ \Rightarrow r=\frac{3}{4} }

Hence option 2 is correct.




 

Posted by

shivangi.shekhar

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