What is the foci x=-3/8 (y-2)^2-1 ?

The foci x=-3/8 (y-2)^2-1 is (-5/3 ,2)

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foci x=-3/8 (y-2)^2-1

foci

x = - \frac{3}{8} (y - 2)^{2} - 1

(- \frac{5}{3}, 2)

Solution steps

Rewrite

x = - \frac{3}{8} (y - 2)^{2} - 1

in the standard form:

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

(h, k) = (- 1, 2), p = - \frac{2}{3}

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

p

from the center

(- 1, 2)

along the x-axis

(- 1 + p, 2)

= (- 1 + (- \frac{2}{3}), 2)

Refine

(- \frac{5}{3}, 2)

y = 3 x^{2} - 7

y = p (x - h)^{2} + k

(x - 3)^{2} = - 12 y

y = 3 x^{2} + 6

y = 2 x^{2} - x