What is the foci 12x^2-72x+77 ?

The foci 12x^2-72x+77 is (3,-1487/48)

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foci 12x^2-72x+77

foci

12 x^{2} - 72 x + 77

(3, - \frac{1487}{48})

Solution steps

Rewrite

y = 12 x^{2} - 72 x + 77

in the standard form

4 \cdot \frac{1}{48} (y - (- 31)) = (x - 3)^{2}

(h, k) = (3, - 31), p = \frac{1}{48}

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

p

from the center

(3, - 31)

along the y-axis

(3, - 31 + p)

= (3, - 31 + \frac{1}{48})

Refine

(3, - \frac{1487}{48})

y^{2} - 10 x + 4 y - 16 = 0

x^{2} - 4 x - 5

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

x^{2} + 4 x - 8 y + 12 = 0

y = x^{2} + x + 1