What is the foci y=(9x^2)/2 ?

The foci y=(9x^2)/2 is (0, 1/18)

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foci y=(9x^2)/2

foci

y = \frac{9 x ^{2}}{2}

(0, \frac{1}{18})

Solution steps

Rewrite

y = \frac{9 x ^{2}}{2}

in the standard form:

4 \cdot \frac{1}{18} (y - 0) = (x - 0)^{2}

(h, k) = (0, 0), p = \frac{1}{18}

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}{18})

Refine

(0, \frac{1}{18})

- (x + 1)^{2} + 4

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

(x + 2)^{2} = - 12 (y + 2)

y = \frac{1}{64} s^{2}

92 x^{2}