question_answer

Let \[P(3,3)\] and \[Q(2,1)\] be two points and the straight lines PQ and QR are equally inclined to the circle\[{{x}^{2}}+{{y}^{2}}=5,\] then equation of the line QR is

A) \[2x-11y=15\]             

B) \[2x+11y=15\]

C) \[2x+11y+15=0\]     

D)  \[11x-2y=15\]

Correct Answer: B

Solution :

PQ and QR making same angles with the tangent line at \[Q(2,1)\] \[\therefore \left| \frac{m-\frac{1}{2}}{1+m\cdot \frac{1}{2}} \right|=\left| \frac{2-\frac{1}{2}}{1+2\cdot \frac{1}{2}} \right|\] \[\left| \frac{2m-1}{m+2} \right|=\frac{3}{4}\Rightarrow m=2\] or \[\frac{-\,2}{11}\] Equation of QR is, \[(y-1)=\frac{-2}{11}(x-2)\] \[2x+11y=15\]