question_answer

A circle passes through the points (2, 2) and (9, 9) and touches the x-axis. The absolute value of the difference of x-coordinate of the point of contact is

A)  \[-6\]                           

B)  4

C)  6                                

D)  12

Correct Answer: D

Solution :

Any through (2, 2) and (9, 9) is       ?(1) For the point of intersection with x-axis, we put y = 0 in (1), we get \[(x-2)(x-9)\,+18-\lambda x=0\] Put discriminate = 0 \[\Rightarrow \,{{(11+\lambda )}^{2}}-4(36)=0\,\Rightarrow \,\lambda =-23,1\] \[\therefore \,\,x=\frac{11+\lambda }{2}=\pm 6\] So, the absolute value of the difference of x-coordinate of the point of contact = |6-(-6)|=12