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  • The chord of contact of the pair of tangents drawn from each point on the line <img alt="\mathrm{2 x+4 y-4=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%20x&plus;4%20y-

The chord of contact of the pair of tangents drawn from each point on the line \mathrm{2 x+4 y-4=0}  to the circle \mathrm{x^{2}+y^{2}=1} pass through the point

Option: 1

(1,2)


Option: 2

\left(\frac{1}{2}, 1\right)


Option: 3

\left(\frac{1}{2}, \frac{1}{4}\right)


Option: 4

 none of these


Answers (1)

best_answer

 Consider the point (\alpha, 4-2 \alpha) on the line \mathrm{2 x+y=4}.  The chord of contact if the tangents from this point is \mathrm{\mathrm{S}_{1}=0}

\mathrm{\alpha \mathrm{x}+(4-2 \alpha) \mathrm{y}-1=0}
\mathrm{\Rightarrow \alpha(\mathrm{x}-2 \mathrm{y})+(4 \mathrm{y}-1)=0}
\Rightarrow The lines are concurrent at the point \left(\frac{1}{2}, \frac{1}{4}\right)

Posted by

sudhir kumar

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