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If the lines \mathrm{(y-b)=m_{1}(x+a)} and \mathrm{(y-b)=m_{2}(x+a)} are the tangents of \mathrm{y^{2}= 4ax}, then

Option: 1

\mathrm{m_{1}+m_{2}=0}


Option: 2

\mathrm{m_{1} m_{2}=1}


Option: 3

\mathrm{m_{1} m_{2}=-1}


Option: 4

\mathrm{m_{1}+m_{2}=1}


Answers (1)

best_answer

Clearly, both the lines pass through \mathrm{(-a, b)} which is a point lying on the directrix of the parabola.

Thus, \mathrm{m_{1} m_{2}=-1}.

Because tangents drawn from any point on the directrix are always mutually perpendicular.

Posted by

Ritika Harsh

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