What is the foci 0.3x^2-66x+23114 ?

The foci 0.3x^2-66x+23114 is (110,19484.83333…)

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foci 0.3x^2-66x+23114

foci

0.3 x^{2} - 66 x + 23114

(110, 19484.83333 \dots)

Solution steps

Rewrite

y = 0.3 x^{2} - 66 x + 23114

in the standard form

4 \cdot 0.83333 \dots (y - 19484) = (x - 110)^{2}

(h, k) = (110, 19484), p = 0.83333 \dots

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

p

from the center

(110, 19484)

along the y-axis

(110, 19484 + p)

= (110, 19484 + 0.83333 \dots)

Refine

(110, 19484.83333 \dots)

\frac{x}{25} - y^{2} = 1

y = 2 x^{2} - 2

x^{2} + 2 x - 1 - (2 x^{2} - 3 x + 6)

- x^{2} + 8 x - 12

y = x^{2} + 5 x - 14

What is the foci 0.3x^2-66x+23114 ?
The foci 0.3x^2-66x+23114 is (110,19484.83333…)