question_answer

The length of the chord joining the points in which the straight line \[\frac{x}{3}+\frac{y}{4}=1\]cuts the circle \[{{x}^{2}}+{{y}^{2}}=\frac{169}{25}\]is  [Orissa JEE 2003]

A)            1    

B)            2

C)            4    

D)            8

Correct Answer: B

Solution :

           \[OM=\] length of the perpendicular to the line \[4x+3y=12\] from \[(0,\,0)=\frac{12}{5}\].                    Radius of the circle is \[\frac{13}{5}\].            Required length\[=2\sqrt{\frac{169}{25}-\frac{144}{25}}=2\].