10.    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 a fixed point-        (a)    (2,4)(b)    (-1/2,-1/4)(c)    (1/2, 1/4)(d)    (-2, -4)

Jitender Singh IIT Delhi
8 years ago
Sol:
Let (h, k) be the point on the line from where pair of tangents are drawn.
Equation of chord of contact:
$hx+ky=1$
Also (h, k) lie on the line, we have
$2h+k=4$
$hx+(4-2h)y=4$
Only (1/2, 1/4) satisfying this equation.
Thanks & Regards
Jitender Singh
IIT Delhi