x^2+10x+6y+19=0
You asked:
Investigate the equation: \({x}^{2} + 10 x + 6 y + 19 = 0\).
MathBot Answer:
The graph of the equation \({x}^{2} + 10 x + 6 y + 19 = 0\) is a parabola.
The coordinates of its vertex are: \(\left(-5, 1\right)\)
The coordinates of its focus are: \(\left(-5, - \frac{1}{2}\right)\)
The directrix has equation: \(- \frac{2 y}{3} + \frac{5}{3} = 0\).
The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= -5 + \theta\\y\left(\theta\right) &= 1 - \frac{\theta^{2}}{6}\end{aligned}\]