Question

The mid point of chord $2x+y-5=0$ of the parabola $y^2=4x$ is

• A. $(2,1)$
• B. $(1,3)$
• C. $(3,-1)$
• D. $(\frac{5}{2},0)$

Answer 1

The correct option is C $(3,-1)$

Let, $(h,k)$ be the point where the chord $2x+y-5$ meets the parabola $y^2=4x$.

Then,

$2h+k=5$.....(1) and $k^2=4h$......(2).

Using the value of $h$ from (1) in (2) we get,

$k^2=2(5-k)$

or, $k^2+2k-10=0$

$\Rightarrow k=\frac{-2\pm \sqrt{4+40}}{2}=$ $-1\pm \sqrt{11}$.

For, $k=-1+\sqrt{11},h=3-\frac{\sqrt{11}}{2}$ and for $k=-1-\sqrt{11},h=3+\frac{\sqrt{11}}{2}$.

End points of the chord of the parabola are $(3-\frac{\sqrt{11}}{2},-1+\sqrt{11})$ and $(3+\frac{\sqrt{11}}{2},-1-\sqrt{11})$.

$\therefore$ the mid point of the chord is $(3,-1)$.