Equation of incircle touches x=0 and y=0 is (x−h)2+(y−h)2=h2 Here, radius =h, and centre of circle is (h,h) The circle also touches the line 3x+4y−24=0 |
3h+4h−24
√32+42
|=h 7h−24=±5h 7h−24=5h and 7h−24=−5h h=12 and h=2 (x−2)2+(y−2)2=22 [∵h=12 is not acceptable ] ⇒x2+y2−4x−4y+4=0