Let the centre of a circle, passing through the points (0,0),(1,0) and touching the circle x^2+y^2=9 , be (h, k) . Then for all possible values of the coordinates of the centre (h, k), 4 (h^2+k^2 ) is equal to_________

Step-by-step solution

aligned & ( x - h )^2+( y - k )^2= h ^2+ k ^2 & x ^2+ y ^2-2 hx -2 ky =0 & passes through (1,0) & 1+0-2 ~h =0 & h =1 / 2 & OC = OP 2 & ( 1 2 )^2+ k ^2 = 3 2 aligned aligned & 1 4 + k ^2= 9 4 & k ^2=2 & k = 2 aligned Possible coordinate of aligned & c ( h , k ) ( 1 2 , 2 ) ( 1 2 ,- 2 ) & 4 ( ~h ^2+ k ^2 )=4 ( 1 4 +2 )=4 ( 9 4 )=9 aligned