Question

The chords of contact of the pair of tangents drawn from each point on the line $2x+y=4$ to the circle $x^2+y^2=1$

• A. $(1,2)$
• B. $\left(\frac{1}{2},\frac{1}{4}\right)$
• C. $(2,4)$
• D. $none$

Answer 1

The correct option is A $(1,2)$

Equation of chord of contact

$hx+ky=1$ ..... $\left(i\right)$

$(h,k)$ lie on the line,we have

$2x+y=4$ ...... (Given)

Now, $x$ and $y$ change with $h$ and $k$

$\Rightarrow 2h+k=4$ ...... $\left(ii\right)$

Now put the value of $k=4-2h$ in equation $\left(i\right)$ we get,

$\Rightarrow hx+ky=1$

$\Rightarrow hx+(4-2h)y=1$ [from $\left(i\right)$]

$\Rightarrow hx+4y-2hy=1$

$\Rightarrow hx-2hy+4y-1=0$

$\Rightarrow 4y-1=0$ or $x-2y=0$

$\Rightarrow y=\frac{1}{4}$ or $x=\frac{1}{2}$

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