Question

The mid-point of the chord $2x+y-4=0$ of the parabola $y^2=4x$ is?

• A. $(\frac{5}{2},-1)$
• B. $(-1,\frac{5}{2})$
• C. $(\frac{3}{2},-1)$
• D. None of these

Answer 1

The correct option is A $(\frac{5}{2},-1)$

Let $(h,k)$ be the mid-point of the chord $2x+y-4=0$ of the
parabola $y^2=4x$. Then, its equation is $ky-2(x+h)=k^2-4h$
[using $T=S^{\prime }$]
$\Rightarrow 2x-ky+k^2-2h=0$ ......(i)
Eq. (i) and $2x+y-4=0$ represent the same line.
$\therefore -k=1$ and $k^2-2h=-4$
$\Rightarrow k=-1,h=\frac{5}{2}$
Hence, the required mid-point is $\left(\frac{5}{2},-1\right)$.