What is the directrix F=(mv^2)/r ?

The directrix F=(mv^2)/r is r=-1/(4m)

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directrix F=(mv^2)/r

directrix

F = \frac{m v ^{2}}{r}

r = - \frac{1}{4 m}

Solution steps

Rewrite

F - \frac{m v ^{2}}{r} = 0

in the standard form

4 \cdot \frac{1}{4 m} (r - 0) = (v - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{4 m}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(0, 0)

y-coordinate

r = 0 - p

r = 0 - \frac{1}{4 m}

Refine

r = - \frac{1}{4 m}

- x^{2} + 6 x + 1

y = 3 x^{2} + 1 - (x + 4)

x^{2} = 8 (y + 4)

y = 2 x (x - 9) - (x - 9)

y = 2 x^{2} - 10 x + 12