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 (h,k) then 4(h+k) is

Options

A. (1/2, 1/4)
B. (1/4, 1/2)
C. (1, 1/2)
D. (1/2, 1)

Answer

A

Explanation

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).