What is the foci-0.4x^2-5 ?

The foci-0.4x^2-5 is (0,-5.625)

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foci-0.4x^2-5

foci

- 0.4 x^{2} - 5

(0, - 5.625)

Solution steps

Rewrite

y = - 0.4 x^{2} - 5

in the standard form:

4 (- 0.625) (y - (- 5)) = (x - 0)^{2}

(h, k) = (0, - 5), p = - 0.625

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

p

from the center

(0, - 5)

along the y-axis

(0, - 5 + p)

= (0, - 5 + (- 0.625))

Refine

(0, - 5.625)

x^{2} + 6 x = 4 y - 5

18 x^{2} + y = 0

(x + 1)^{2} = - 3 (y - 6)

y = 3 x^{2} - 11 x + 10

x^{2} + 10 x = - 12 y - 1