L=4 $\pi$ j^2
You asked:
Investigate the equation: \(L = 4 \cdot \pi \cdot {j}^{2}\).
MathBot Answer:
The graph of the equation \(L = 4 \cdot \pi \cdot {j}^{2}\) is a parabola.
The coordinates of its vertex are: \(\left(0, 0\right)\)
The coordinates of its focus are: \(\left(\frac{1}{16 \pi}, 0\right)\)
The directrix has equation: \(16 \pi L + 1 = 0\).
The parabola has parameterization: \[\begin{aligned}L\left(\theta\right) &= 4 \pi \theta^{2}\\j\left(\theta\right) &= \theta\end{aligned}\]