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

The foci (x-1)^2=8(y-k) is (1,k+2)

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foci (x-1)^2=8(y-k)

foci

(x - 1)^{2} = 8 (y - k)

(1, k + 2)

Solution steps

Rewrite

(x - 1)^{2} = 8 (y - k)

in the standard form:

4 \cdot 2 (y - k) = (x - 1)^{2}

(h, k) = (1, k), p = 2

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

p

from the center

(1, k)

along the y-axis

(1, k + p)

= (1, k + 2)

(y - 4)^{2} = 8 (x - 3)

y = 16 x^{2} - 25

+ 2 x^{2} - 3 x - 1

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

2 x^{2} - 5 x + 1