Question

The chord of contact of the pair of tangents to the circle $x^2+y^2=1$ drawn from any points on the line $2x+y=4$ pass trough the point

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

Answer 1

Answer: (A)

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

Let the point be $P(h,k)$
Thus equation chord of contact through P is given by,
$hx+ky=1$. Now comparing this with the the given line $2x+y=4$
$\Rightarrow \frac{h}{2}=\frac{k}{1}=\frac{1}{4}$
Hence required point is $P(\frac{1}{2},\frac{1}{4})$