The absolute difference between the squares of the radii of the two circles passing through the point (-9,4) and touching the lines x+y=3 and x-y=3 , is equal to ______.

Step-by-step solution

Centre ( a , 0) r = | a -0-3 2 | circle (x-a)^2+y^2= ( a-3 2 )^2 passes through (-9,4) 2 (a^2+18 a+81+16 )= (a^2-6 a+9 ) a ^2+42 a +185=0 (a+37)(a+5)=0 a=-37,-5 r₁= | -37-3 2 |=20 2 r ₂= | -5-3 2 |=4 2 |r₁^2-r₂^2 |=|800-32|=768