What is the foci 4x^2-24x-30 ?

The foci 4x^2-24x-30 is (3,-1055/16)

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foci 4x^2-24x-30

foci

4 x^{2} - 24 x - 30

(3, - \frac{1055}{16})

Solution steps

Rewrite

y = 4 x^{2} - 24 x - 30

in the standard form

4 \cdot \frac{1}{16} (y - (- 66)) = (x - 3)^{2}

(h, k) = (3, - 66), p = \frac{1}{16}

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

p

from the center

(3, - 66)

along the y-axis

(3, - 66 + p)

= (3, - 66 + \frac{1}{16})

Refine

(3, - \frac{1055}{16})

3 y^{2} - 6 y - x = 0

- 2 x^{2} - 16 x - 25

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

- x^{2} + 10 x - 23

(y - 2)^{2} = 4 (x + 3)