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Consider the family of circles x^2+y^2-2...

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

4

B

`4 sqrt(2)`

C

6

D

8

Text Solution

Verified by Experts

We have `x^(2)+y^(2) -2x-2ay-8=0`
or `(x^(2)+y^(2)-2x-8)-2ay =0`, which is of the form `S + lambda L =0`.
Solving `S -= x^(2)+y^(2) -2x-8=0` and `L -= y =0`, we get
`x^(2)-2x-8=0`
`implies (x-4) (x+2)=0`
`implies x = - 2` or `4`
`implies A -= (4,0) , B -= (-2,0)`
Distance between A and `B =6`
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