Let $P$ be the point (1,0) and $\mathcal{Q}$ a point on the locus of $y^{2} = 8x,\ \$The locus of mid point of P$\mathcal{Q}$ is

Question

Dr. Abubacker · Accepted Answer

(d)
The coordinates of $P$ are $(1,\ 0)$. A gerneral point$\ \mathcal{Q}\$on $y^{2} = 8x$ is $\left( 2t^{2},\ 4t ight)$. Let mid point of $P\mathcal{Q}$ is$\ (h,\ k)$
$	herefore 2h = 2t^{2} + 1$ and$\ 2k = 4t\  \Rightarrow \ t = \frac{k}{2}$
$	herefore 2h = \frac{2k^{2}}{4} + 1\  \Rightarrow \ 4h = k^{2} + 2\$
Hence, the locus of $(h,\ k)$ is $y^{2} - 4x + 2 = 0$

Q. Let $P$ be the point (1,0) and $\mathcal{Q}$ a point on the locus of $y^{2} = 8x,\ \$The locus of mid point of P$\mathcal{Q}$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?