What is the foci ((x-3)^2)/8+5 ?

The foci ((x-3)^2)/8+5 is (3,7)

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foci ((x-3)^2)/8+5

foci

\frac{( x - 3 ) ^{2}}{8} + 5

(3, 7)

Solution steps

Rewrite

y = \frac{( x - 3 ) ^{2}}{8} + 5

in the standard form:

4 \cdot 2 (y - 5) = (x - 3)^{2}

(h, k) = (3, 5), p = 2

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

p

from the center

(3, 5)

along the y-axis

(3, 5 + p)

= (3, 5 + 2)

Refine

(3, 7)

(x + 5)^{2} + 3

- 0.1 x^{2} + 1.2 x + 98.6

y^{2} - 8 x - 6 y - 3 = 0

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

x = 3 - 5 (y + 1)^{2}