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Let $O$ be the vertex and $Q$ any point on the parabola $x^2=8y$. If point $P$ divides segment $OQ$ internally in the ratio $1:3$, find the locus of $P$.
Let $Q=(4t, 2t^2)$ be a point on $x^2=8y$ (using parametrization $x=4t, y=2t^2$). $O=(0,0)$.
$P$ divides $OQ$ in ratio $1:3$: $P=\left(\frac{1\cdot4t+3\cdot0}{4},\frac{1\cdot2t^2+3\cdot0}{4}\right)=\left(t,\frac{t^2}{2}\right)$
Let $P=(h,k)$: $h=t$ and $k=\frac{t^2}{2}=\frac{h^2}{2}$
So $h^2=2k$, i.e., the locus is $x^2=2y$.
Natural killer (NK) cells are directly activated by which substance?
Interferons (produced in response to viral infections) activate NK cells, enhancing their cytotoxic activity against virus-infected cells and tumor cells.
The 18th Amendment to the Constitution of Pakistan (2010) primarily focused on:
The 18th Amendment significantly increased provincial autonomy and removed the President's power to dissolve Parliament.
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