What is the foci 6x^2-24x-30 ?

The foci 6x^2-24x-30 is (2,-1295/24)

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foci 6x^2-24x-30

foci

6 x^{2} - 24 x - 30

(2, - \frac{1295}{24})

Solution steps

Rewrite

y = 6 x^{2} - 24 x - 30

in the standard form

4 \cdot \frac{1}{24} (y - (- 54)) = (x - 2)^{2}

(h, k) = (2, - 54), p = \frac{1}{24}

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

p

from the center

(2, - 54)

along the y-axis

(2, - 54 + p)

= (2, - 54 + \frac{1}{24})

Refine

(2, - \frac{1295}{24})

x^{2} + y = 4

y = x^{2} - 4 x - 12

x^{2} = - y

(y - 2)^{2} = (x - 1)^{2} + (y + 4)^{2}

x^{(2)} - 6 x + 5 y = - 34