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Find the circle passing through the foci of the ellipse $\dfrac{x^2}{16}+\dfrac{y^2}{9}=1$ and having its centre at $(0,3)$.
For the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$: $a^2=16, b^2=9$, so $c^2=16-9=7$, giving foci at $(\pm\sqrt{7},0)$.
The circle has centre $(0,3)$. Radius $r=$ distance from $(0,3)$ to $(\sqrt{7},0)$:
$r^2=(\sqrt{7}-0)^2+(0-3)^2=7+9=16\Rightarrow r=4$
Equation: $x^2+(y-3)^2=16\Rightarrow x^2+y^2-6y+9=16\Rightarrow x^2+y^2-6y-7=0$
When organizations ask HR managers for assistance in 'matching the distinctive competencies of the firm's human resources to the mission of the organization,' this represents:
This represents strategic HR management - aligning human resources (their distinctive competencies) with organizational strategy (mission). It moves HR from purely operational/administrative functions to strategic business partner role.
Work done = $Q \times V_{origin}$, where $V_{origin}$ is the potential at origin due to the four charges.
Distances from origin:
- $(0,2)$: $r_1 = 2$
- $(0,-2)$: $r_2 = 2$
- $(4,2)$: $r_3 = \sqrt{16+4} = \sqrt{20} = 2\sqrt{5}$
- $(4,-2)$: $r_4 = \sqrt{20} = 2\sqrt{5}$
$V = \frac{Q}{4\pi\varepsilon_0}\left(\frac{1}{2}+\frac{1}{2}+\frac{1}{2\sqrt{5}}+\frac{1}{2\sqrt{5}}\right) = \frac{Q}{4\pi\varepsilon_0}\left(1 + \frac{1}{\sqrt{5}}\right)$
Work $= QV = \dfrac{Q^2}{4\pi\varepsilon_0}\left(1+\dfrac{1}{\sqrt{5}}\right)$
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