What is the foci y=(3*1/2 x^2)/2 ?

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

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foci y=(3*1/2 x^2)/2

foci

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

(0, \frac{1}{3})

Solution steps

Rewrite

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

in the standard form:

4 \cdot \frac{1}{3} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{3}

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{1}{3})

Refine

(0, \frac{1}{3})

5 x^{2} + 3

(x - 2)^{2} = 4 (y - 2)

y = 3 x^{2} - 6 x + 5

2 x^{2} - 12 x - 5

(x - 5) (x - 3)