What is the foci (x-3)^2=8(y-5) ?

The foci (x-3)^2=8(y-5) is (3,7)

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foci (x-3)^2=8(y-5)

foci

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

(3, 7)

Solution steps

Rewrite

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

y^{2} = - 24 x

- x^{2} + 5 x - 7

y = \frac{6 x}{7} \frac{4 x}{3}

y = 4 x^{2}

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