Question

The chords of contact of the pair of tangents drawn from points on the line $2x+y=4$ to the circle $x^2+y^2=1$ passes through a fixed point $M(x_0,y_0)$ . The value of $(x_0+6y_0)$ is equal to :

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$\begin{array}{c}\frac{x\left(4-h\right)}{2}+hy=1\\ 2x-\frac{hx}{2}+hy=1\\ \left(2x-1\right)+h\left(y-\frac{x}{2}\right)=0\\ x=\frac{1}{2}\\ y=\frac{x}{2}\Rightarrow \frac{1}{4}\\ \left(\frac{1}{2},\frac{1}{4}\right)=\left(x_0,y_0\right)\\ x_0+6y_0=\frac{1}{2}+\frac{6}{4}=2\end{array}$

Hence,

Option $C$ is correct answer.