What is the foci y=-x^2+14x+49 ?

The foci y=-x^2+14x+49 is (7, 391/4)

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foci y=-x^2+14x+49

foci

y = - x^{2} + 14 x + 49

(7, \frac{391}{4})

Solution steps

Rewrite

y = - x^{2} + 14 x + 49

in the standard form

4 (- \frac{1}{4}) (y - 98) = (x - 7)^{2}

(h, k) = (7, 98), p = - \frac{1}{4}

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

p

from the center

(7, 98)

along the y-axis

(7, 98 + p)

= (7, 98 + (- \frac{1}{4}))

Refine

(7, \frac{391}{4})

2 x^{2} - 4 x + 15

x^{2} - 4 x + 5

x^{2} - 4 x + 2

y^{2} + 8 y + 4 x + 20 = 0

(y + 5)^{2} = - 12 (x - 2)