If A B is a focal chord of x^2-2x+y-2=0 ...

If `A B` is a focal chord of `x^2-2x+y-2=0` whose focus is `S` and `A S=l_1,` then find `B Sdot`

`(l_(1))/(2l_(1)-1)`

`(l_(1))/(4l_(1)-1)`

`(l_(1))/(2l_(1)+1)`

None of these

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The correct Answer is:

`x^(2)-2x+y-2=0`
`rArrx^(2)-2x+1=3-y`
`rArr(x-1)^(2)=-(y-3).`
Length of its latus rectum is 1 unit.
Since AS, `(1)/(2)`, BS are in H.P., thus
`(1)/(2)=(ASxxBS)/(AB+BS)rArrBS=(1)/(4I_(1)-I)`

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