Question

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. (2, 1)
• B. (1, 2)
• C. $(\frac{1}{2},\frac{1}{4})$
• D. $(\frac{1}{4},\frac{1}{2})$

Answer 1

The correct option is C $(\frac{1}{2},\frac{1}{4})$

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. $(\frac{1}{2},\frac{1}{4})$.