Question

Let $P$ be the point $(1,0)$ and $Q$ be a point on the curve $y^2=8x$. Then the locus of the mid-point of $PQ$ is

• A. $y^2+4x+2=0$
• B. $y^2-4x+2=0$
• C. $x^2-4y+2=0$
• D. $x^2+4y+2=0$

Answer 1

The correct option is B $y^2-4x+2=0$

Let $R(h,k)$ be the mid-point of $PQ$.
By mid-point formula,
$Q$ is $(2h-1,2k)$


Since $Q$ lies on $y^2=8x$,
$(2k{)}^2=8(2h-1)$
$\Rightarrow k^2=2(2h-1)$
Hence, locus of $Q$ is
$y^2=2(2x-1)$
$\Rightarrow y^2-4x+2=0$