The radius of the largest circle lying in the first quadrant and touching the line 4x+3y-12=0 and the co ordinate axis is?

1 Answer
CW
Apr 14, 2018

#6# units

Explanation:

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A circle with a radius #r# lying in the first quadrant and touching the coordinate axes has a center #C=(r,r)#, as shown in the figure.
Recall that the distance between a point #P(x_0,y_0)# and a line #L: ax+by+c=0# is :
#d=|ax_0+by_0+c|/sqrt(a^2+b^2)#
Given that the circle also touches the line #4x+3y-12=0#,
#=># the distance #r# from point #C(r,r)# to line #4x+3y-12=0# is :
#r=|4r+3r-12|/sqrt(4^2+3^2)#
#=> r=|7r-12|/5, => r=1 or 6# units,

Hence, the largest radius #r=6# units

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