Question

The radius of the largest circle lying in the first quadrant, touching $4x+3y=12$ and co-ordinate axes is

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is B $6$

Centre of circle touching both axis is at (a,a), distance of (a,a) from 4x+3y-12=0 is a.
$radius=a=\left|\frac{4a+3a-12}{5}\right|$
$5a=|7a-12|$
$5a=7a-12$ or $-5a=7a-12$
$a=6ora=1$
$\Rightarrow radius=a$
So, largest circle have radius$=a=6$