What is the foci y=-x^2-6x-5 ?

The foci y=-x^2-6x-5 is (-3, 15/4)

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foci y=-x^2-6x-5

foci

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

(- 3, \frac{15}{4})

Solution steps

Rewrite

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

in the standard form

4 (- \frac{1}{4}) (y - 4) = (x - (- 3))^{2}

(h, k) = (- 3, 4), p = - \frac{1}{4}

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

p

from the center

(- 3, 4)

along the y-axis

(- 3, 4 + p)

= (- 3, 4 + (- \frac{1}{4}))

Refine

(- 3, \frac{15}{4})

y^{2} = 6 x

y^{2} + 8 x - 6 y = - 25

2 x^{2} - 19 x + 9

(x + 5)^{2} = - 20 (y - 2)

x^{2} + 6 x - 8 y + 1 = 0