Let a circle C pass through the points (4,2) and (0,2) , and its centre lie on 3 x+2 y+2=0 . Then the length of the chord, of the circle C , whose mid-point is (1,2) , is :

Step-by-step solution

Let the centre be (-2 a, 6 a-2 2 ) (-2 a, 3 a-1) Centre is equal distance from (4,2) and (0,2) aligned & (4+2 a)^2+(3 a-3)^2 = (-2 a-0)^2+(3 a-3)^2 & (2 a+4)^2+9(a-1)^2=4 a^2+9(a-1)^2 & 4 a^2+16+16 a=4 a^2 a=-1 & centre (2,-4) Radius = 40 aligned aligned & A M^2=( 40 )^2-( 37 )^2 & 2 A M=A B=2 3 aligned