What is the foci 5x^2+210x-34775 ?

The foci 5x^2+210x-34775 is (-21,-739599/20)

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foci 5x^2+210x-34775

foci

5 x^{2} + 210 x - 34775

(- 21, - \frac{739599}{20})

Solution steps

Rewrite

y = 5 x^{2} + 210 x - 34775

in the standard form

4 \cdot \frac{1}{20} (y - (- 36980)) = (x - (- 21))^{2}

(h, k) = (- 21, - 36980), p = \frac{1}{20}

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

p

from the center

(- 21, - 36980)

along the y-axis

(- 21, - 36980 + p)

= (- 21, - 36980 + \frac{1}{20})

Refine

(- 21, - \frac{739599}{20})

x^{2} = - 28 y

y = 9 - x^{2}

2 x^{2} + x - 6

y = 2 x^{2} - 6 x + 10

y = x^{2} - x - 6