What is the foci y=9-(x-2)^2 ?

The foci y=9-(x-2)^2 is (2, 35/4)

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foci y=9-(x-2)^2

foci

y = 9 - (x - 2)^{2}

(2, \frac{35}{4})

Solution steps

Rewrite

y = 9 - (x - 2)^{2}

in the standard form:

4 (- \frac{1}{4}) (y - 9) = (x - 2)^{2}

(h, k) = (2, 9), p = - \frac{1}{4}

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

p

from the center

(2, 9)

along the y-axis

(2, 9 + p)

= (2, 9 + (- \frac{1}{4}))

Refine

(2, \frac{35}{4})

x^{2} = 6 y

y = x^{2} - 2 x 5

y = x^{2} + 3 x - 16

y = (5 x - 7)^{2} - 13

4 x^{2} - 12 x - 16 y + 41 = 0