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 the point .......

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Solution

$(\frac{1}{2}, \frac{1}{4})$
Let $(h, k)$ be any point on the given line
$∴ 2 h + k = 4$ and C.C. is $h x + k y = 1$
or $h x + (4 - 2 h) y = 1 ∵ k = 4 - 2 h$
or $(4 y - 1) + h (x + 2 y) = 0$
It is of the form $P + λ Q = 0$ . It passes through the intersection of $P = 0$ and $Q = 0$ or $(\frac{1}{2}, \frac{1}{4})$ .

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