What is the foci 12x^2+12x+1 ?

The foci 12x^2+12x+1 is (-1/2 ,-95/48)

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foci 12x^2+12x+1

foci

12 x^{2} + 12 x + 1

(- \frac{1}{2}, - \frac{95}{48})

Solution steps

Rewrite

y = 12 x^{2} + 12 x + 1

in the standard form

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

(h, k) = (- \frac{1}{2}, - 2), p = \frac{1}{48}

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

p

from the center

(- \frac{1}{2}, - 2)

along the y-axis

(- \frac{1}{2}, - 2 + p)

= (- \frac{1}{2}, - 2 + \frac{1}{48})

Refine

(- \frac{1}{2}, - \frac{95}{48})

- x^{2} + 8 x - 13

x^{2} = - 9 y

+ 4 t^{2}

(- 4 x - 11)^{2}

2 x^{2} - 8 x + 3