The centers of the circles touching both the coordinate axes lies on the line

x – y = 0 or x + y = 0 according to the quadrant in which the circle lies.

Based on this data answer the following 2 questions.

A) If the difference between the radii of the circles passing through (a, b) and touching the axes is c>0 and a, b >  0 then the least value of a + b is

 

 

1 right parenthesis space c space space space space space space space space space space space 2 right parenthesis space square root of 2 space c space space space space space space space space space space 3 right parenthesis space fraction numerator c over denominator square root of 2 end fraction space space space space space space space space space space 4 right parenthesis thin space 2 c

B) If one of the points of intersection of the two circles touching the axes is (p,q) then the length of the common chord is

1 right parenthesis thin space space vertical line space p plus-or-minus q vertical line space space space space space space space space space space space 2 right parenthesis square root of 2 space vertical line p plus-or-minus q vertical line space space space space space space space space 3 right parenthesis space 2 space vertical line p plus-or-minus q vertical line space space space space space space space space space 4 right parenthesis thin space square root of 2 space space vertical line p q vertical line

 

 

Asked by Sunil Soni | 10th Aug, 2016, 07:07: PM

Expert Answer:

As the circles touches the axes so, the point of intersection will always lie on axis.
So either x coordinate or y coordinate will be zero.
And the length of common cord will also bezero.
 
Only option (4) satisfies the above two conditions.
 
 
Please post one query at a time.

Answered by Vijaykumar Wani | 12th Aug, 2016, 05:34: PM