\(A = \frac{\sqrt{3}}{4} \times l^2\)
You asked:
Investigate the equation: \(A = \frac{\sqrt{3}}{4} {l}^{2}\).
MathBot Answer:
The graph of the equation \(A = \frac{\sqrt{3}}{4} {l}^{2}\) is a parabola.
The coordinates of its vertex are: \(\left(0, 0\right)\)
The coordinates of its focus are: \(\left(\frac{\sqrt{3}}{3}, 0\right)\)
The directrix has equation: \(\sqrt{3} A + 1 = 0\).
The parabola has parameterization: \[\begin{aligned}A\left(\theta\right) &= \frac{\sqrt{3} \theta^{2}}{4}\\l\left(\theta\right) &= \theta\end{aligned}\]