What is the foci (y-2)^2=8(x-5) ?

The foci (y-2)^2=8(x-5) is (7,2)

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foci (y-2)^2=8(x-5)

foci

(y - 2)^{2} = 8 (x - 5)

(7, 2)

Solution steps

Rewrite

(y - 2)^{2} = 8 (x - 5)

in the standard form:

4 \cdot 2 (x - 5) = (y - 2)^{2}

(h, k) = (5, 2), p = 2

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

p

from the center

(5, 2)

along the x-axis

(5 + p, 2)

= (5 + 2, 2)

Refine

(7, 2)

(x + 1)^{2} = (y + 4)

y = - x^{2} + 4 x + 3

x^{2} - 4 x - 5 y + 7 = 0

(x - 2)^{2} = 12 (y - 1)

x^{2} - 2 x - 4