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

The foci (x-3)^2=8(y-2) is (3,4)

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

foci

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

(3, 4)

Solution steps

Rewrite

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

in the standard form:

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

(h, k) = (3, 2), p = 2

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

p

from the center

(3, 2)

along the y-axis

(3, 2 + p)

= (3, 2 + 2)

Refine

(3, 4)

(x + 3)^{2} = 24 (y - 1)

3 - 2 x - x^{2}

x^{2} + x - 1

y = - x^{2} + 2

(y - 5)^{2} = 12 (x + 3)