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The chords of contact of the pair of tan...

The chords of contact of the pair of tangents drawn from each point on the line `2x + y=4` to the circle `x^2 + y^2=1` pass through the point (a,b) then 4(a+b) is

A

(1/2, 1/4)

B

(1/4, 1/2)

C

(1, 1/2)

D

(1/2, 1)

Text Solution

Verified by Experts

The correct Answer is:
A
Let P(t, 4-2t) be any point of the line 2x+y=4.
The equation of the chord of contact of tangents drawn from P to the circle `x^(2)+y^(2)=1` is
`tx+(4-2t)y=1rArr(4y-1)+t(x-2y)=0`
Clearly, it passes through the point of intersection of the lines 4y-1=0 and x-2y=0 i.e. (1/2, 1/4).
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