What is the foci+(1/2 x-1)^2-2 ?

The foci+(1/2 x-1)^2-2 is (2,-1)

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foci+(1/2 x-1)^2-2

foci

+ (\frac{1}{2} x - 1)^{2} - 2

(2, - 1)

Solution steps

Rewrite

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

in the standard form:

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

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

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

p

from the center

(2, - 2)

along the y-axis

(2, - 2 + p)

= (2, - 2 + 1)

Refine

(2, - 1)

x^{2} + x - 5

x^{2} + x - 4

(x + 6)^{2} = 9 (y - 1)

x^{2} - 2 x - 6 y - 5 = 0

81 y^{2}