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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`

Text Solution

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`x^(2)-2x+y-2=0`
`orx^(2)-2x+1=3-y`
`or(x-1)^(2)=-(y-3)`
The length of its latus rectum is 1 unit.
Since AS, 1/2, and BS are in HP, we have
`(1)/(2)=(2ASxxBS)/(AS+BS)`
`or" "BS=(l_(1))/((4l_(1)-1))`
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