Question

The chord of contact of the pair of tangents to the circle $x^2+y^2=1$ drawn from any point on the line $2x+y=4$ passes through a fixed point.

• A. True
• B. False

Answer 1

The correct option is A True

If chords are drawn to the circle from a fixed point $(x_1,y_1)$ and then tangents are drawn at point of contact, the point of intersection of all tangents lie on a fixed point.

The fixed point is called pole and fixed line is called polar.

Equation of polar is $T=0$.

$C:x^2+y^2-1=0$

Equation of polar is $T=0$.

$x{x}_1+y{y}_1-1=0$

The line is identical to given line $2x+y-4=0$.

By comparing coefficients, we get,

$\frac{x_1}{2}=\frac{y_1}{1}=\frac{-1}{-4}$

$x_1=\frac{1}{2},y_1=\frac{1}{4}$

Hence, the fixed point is $(\frac{1}{2},\frac{1}{4})$.