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 a fixed point

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

Answer 1

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

The chord of contact of tangent from $(\alpha ,\beta )$ is

$\alpha x+\beta y=1$ .........$\left(1\right)$

Also, $(\alpha ,\beta )$ lies on $2x+y=4$

so $2\alpha +\beta =4$

$\Rightarrow \frac{\alpha }{2}+\frac{\beta }{4}=1$

Hence $\left(1\right)$ pases through $(\frac{1}{2},\frac{1}{4})$