What is the foci y=-x^2+44x+1 ?

The foci y=-x^2+44x+1 is (22, 1939/4)

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foci y=-x^2+44x+1

foci

y = - x^{2} + 44 x + 1

(22, \frac{1939}{4})

Solution steps

Rewrite

y = - x^{2} + 44 x + 1

in the standard form

4 (- \frac{1}{4}) (y - 485) = (x - 22)^{2}

(h, k) = (22, 485), p = - \frac{1}{4}

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

p

from the center

(22, 485)

along the y-axis

(22, 485 + p)

= (22, 485 + (- \frac{1}{4}))

Refine

(22, \frac{1939}{4})

- 16 t^{2} + 60 t + 3

y = \frac{x ^{3}}{x}

(y - 2)^{2} = 12 (x + 4)

10 x^{2} - 19 x + 5

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