What is the foci y=-1/3 x^2 ?

The foci y=-1/3 x^2 is (0,-3/4)

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foci y=-1/3 x^2

foci

y = - \frac{1}{3} x^{2}

(0, - \frac{3}{4})

Solution steps

Rewrite

y = - \frac{1}{3} x^{2}

in the standard form:

4 (- \frac{3}{4}) (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = - \frac{3}{4}

Parabola is symmetric around the y-axis and so the focus lies a distance

p

from the center

(0, 0)

along the y-axis

(0, 0 + p)

= (0, 0 + (- \frac{3}{4}))

Refine

(0, - \frac{3}{4})

x^{2} = 8 y + 2 x - 33

(x - 4)^{2} = 20 (y + 5)

y = \frac{1}{2} (1 - 2 x - x^{2})

y = \frac{1}{4} (x + 3)^{2} - 5

- 2 x^{2} + 3 x