Circle `x^2 + y^2 - 2x - lambdax - 1 = 0` passes through to fixed points, coordinates of the points are

Consider the family of circles x^(2)+y^(2)-2x-2 lambda y-8=0 passing through two fixed points AandB .Then the distance between the points AandB is

The normal to-be circle x^2 +y^2 - 4x + 6y -12=0 passes through the point

Consider the family of circles x^2+y^2-2x-2lambda-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

Consider the family of circles x^2+y^2-2x-2lambday-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

Consider the family of circles x^2+y^2-2x-2lambday-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

Consider the family of circles x^2+y^2-2x-2lambday-8=0 passing through two fixed points Aa n dB . Then the distance between the points Aa n dB is_____

A variable circle always touches the line y =x and passes through the point ( 0,0). The common chords of above circle and x^(2) +y^(2)+ 6x + 8 y -7 =0 will pass through a fixed point whose coordinates are :

Prove that chord of contact of the pair of tangents to the circle x^(2)+y^(2)=1 drawn from any point on the line 2x+y=4 passes through a fixed point.Also,find the coordinates of that point.

Show that the straight lines x(a+2b)+y(a+3b)=a+b of a and b pass through a fixed point.Find the coordinates of the fixed point.