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
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