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If the line \mathrm{x+y-1=0} touches the parabola \mathrm{y^{2}=k x}, then the value of \mathrm{k} is

Option: 1

4


Option: 2

-4


Option: 3

2


Option: 4

-2


Answers (1)

best_answer

Any tangent to \mathrm{y^{2}=k x} is;

\mathrm{y=m x+k / 4 m}

Comparing it with the given line \mathrm{y=1-x},
we get,  \mathrm{\mathrm{m}=-1\: and \: \mathrm{k} / 4 \mathrm{~m}=1 \Rightarrow \mathrm{k}=-4}
Alternative Solution:
If \mathrm{x+y-1=0} touches \mathrm{y^{2}=k x}, then \mathrm{y^{2}=k(1-y)} would have equal roots
\mathrm{\Rightarrow \mathrm{k}^{2}+4 \mathrm{k}=0}
\mathrm{\Rightarrow \mathrm{k}=0\: or -4\: but\: \mathrm{k} \neq 0}

hence  \mathrm{k=-4}

Hence (B) is the correct answer.

Posted by

Irshad Anwar

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