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Question

The radius of the larger circle in the first quadrant and touching the line 4x+3y−12=0 and the co-ordinate axes is

A
5
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B
6
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C
7
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D
8
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Solution

The correct option is B 6
Equation of circle touching coordinate axes in 1st Quadrant is given by -
S: (xr)2+(yr)2=r2
Circle S also touches the line 4x+3y12=0
Then the distance of (r,r) from 4x+3y12=0 is r
r=4r+3r125
5r=|7r12|
5r=7r12 or 5r=127r
r=6 or r=1
Thus, the radius of larger circle is r=6.
57695_33314_ans_6011dcd171db45e9a4b22a17ec1047b6.png

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