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_____

Answer

6

Explanation

`x^(2)+y^(2)-2x-2lambda y -8=0`
or `(x^(2)+y^(2)-2x-8)-2 lambda y =0`
which is of the form of `S + lambda L =0`
All the circles pass through the point of intersection of the circle `x^(2)+y^(2)-2x-8=0` and `y=0`
Solving, we gt
`x^(2)-2x+8=0` or `(x-4)(x+2) =0`
`:. A -= (4,0)` and `B -= (-2,0)`
So, the distance between A and B is 6.