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The radius of a circle whose tangents are \mathrm{2 x+3 y-9=0} and \mathrm{4 x+6 y+19= 0} is

Option: 1

\frac{23}{2 \sqrt{17}}


Option: 2

\frac{39}{4 \sqrt{15}}


Option: 3

\frac{41}{3 \sqrt{13}}


Option: 4

\frac{37}{4 \sqrt{13}}


Answers (1)

best_answer

Tangents are \mathrm{ 2 x+3 y-9=0} and \mathrm{ 2 x+3 y+\frac{19}{2}=0}

Distance between these two lines \mathrm{=\frac{\frac{19}{2}+9}{\sqrt{4+9}}=\frac{37}{2 \sqrt{13}}} (Diameter of circle)

                                           \mathrm{\text { So radius }=\frac{37}{4 \sqrt{13}}}

Posted by

Ritika Kankaria

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