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\mathrm{A B} is focal chord of \mathrm{x^{2}-2 x+y-2=0} whose focus is \mathrm{'S'}. If \mathrm{A S= \ell _{1}} then \mathrm{BS} is equal to

Option: 1

\frac{4 \ell_{1}}{4 \ell_{1}-1}


Option: 2

\frac{l_{1}}{4 \ell_{1}-1}


Option: 3

\frac{2 \ell_{1}}{4 \ell_{1}-1}


Option: 4

None of these


Answers (1)

best_answer

\mathrm{x^{2}-2 x+y-2=0}

\mathrm{\Rightarrow \quad x^{2}-2 x+1=3-y }
\mathrm{\Rightarrow \quad(x-1)^{2}=-(y-3) }

Length of it's latus rectum is 1 unit.
Since AS, \mathrm{\frac{1}{2} }, BS are in H.P., therefore

\mathrm{\frac{1}{2} =\frac{2 \cdot A S \cdot B S}{A S+B S} }
\mathrm{\Rightarrow \quad B S =\frac{l_{1}}{\left(4 l_{1}-1\right)} }

Posted by

manish painkra

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