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The chords of contact of the pair of tangents drawn from each point on the line 2 x+y=4 to the circle x^2+y^2=1 pass through fixed point
 

Option: 1

(2,4)


Option: 2

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


Option: 3

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


Option: 4

(-2,-4)


Answers (1)

best_answer

The chord of contact of tangents from (\alpha, \beta) is

\alpha x+\beta y=1    ......(1)
Also, (\alpha, \beta) lies on  2 x+y=4, so that 2 \alpha+\beta=4

\Rightarrow \frac{\alpha}{2}+\frac{\beta}{4}=1
Hence, (1) passes through \left(\frac{1}{2}, \frac{1}{4}\right)

Posted by

Gaurav

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