x-10y=x^2

asked by guest
on Jan 10, 2025 at 5:03 am



You asked:

Investigate the equation: \(x - 10 y = {x}^{2}\).

MathBot Answer:

The graph of the equation \(x - 10 y = {x}^{2}\) is a parabola.

The coordinates of its vertex are: \(\left(\frac{1}{2}, \frac{1}{40}\right)\)

The coordinates of its focus are: \(\left(\frac{1}{2}, - \frac{99}{40}\right)\)

The directrix has equation: \(- \frac{2 y}{5} + \frac{101}{100} = 0\).

The parabola has parameterization: \[\begin{aligned}x\left(\theta\right) &= \frac{1}{2} + \theta\\y\left(\theta\right) &= \frac{1}{40} - \frac{\theta^{2}}{10}\end{aligned}\]

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