1 − 3x^2 = -y
You asked:
Investigate the equation: \(1 - 3 \cdot {x}^{2} = -y\).
MathBot Answer:
The graph of the equation \(1 - 3 \cdot {x}^{2} = -y\) is a parabola.
The coordinates of its vertex are: \(\left(0, -1\right)\)
The coordinates of its focus are: \(\left(0, - \frac{11}{12}\right)\)
The directrix has equation: \(12 y + 13 = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \theta\\y\left(\theta\right) &= -1 + 3 \theta^{2}\end{aligned}\]