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Question

The chords of contact of the pair of tangents drawn from each point on the line
2x+y=4 to the circle x2+y2=1 pass through the point ___.

A
(2, 1)
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B
(1, 2)
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C
(12,14)
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D
(14,12)
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Solution

The correct option is C (12,14)
Let (h, k) be any point on the given line.
Then, 2h+k=4.
Chord of contact to circle from (h, k) is hx + ky = 1
or hx + (4-2h)y = 1
or (4y-1) + h(x-2y) = 0
It passes through the point of intersection of 4y - 1 = 0 and x - 2y = 0
i.e. (12,14).

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