question_answer

If the line \[3x+4y-24=0\] intersects the x-axis at the point A and the y-axis at the point B, then the in centre of the triangle OAB, where 0 is the origin, is- [JEE Main Online Paper (Held On 10-Jan-2019 Morning]

A) (3, 4)                            

B) (2, 2)

C) (4, 4)    

D)                  (4, 3)

Correct Answer: B

Solution :

  Circle C(r, r), radius r,  \[3x+4y-24=0\] tangent \[p=r\] \[\left| \frac{3r+4r-24}{5} \right|\,\,=\,\,r\] \[\left| 7r\,\text{-}\,24 \right|=5r\] \[7r-24=\pm \,5r\text{ };\text{ }r\,\,=\,\,6\,\,(not\,\,possible);\,\,r=2\] centre (2, 2)