What is the foci 5x^2+30x+24y=51 ?

The foci 5x^2+30x+24y=51 is (-3, 14/5)

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foci 5x^2+30x+24y=51

foci

5 x^{2} + 30 x + 24 y = 51

(- 3, \frac{14}{5})

Solution steps

Rewrite

5 x^{2} + 30 x + 24 y = 51

in the standard form

4 (- \frac{6}{5}) (y - 4) = (x - (- 3))^{2}

(h, k) = (- 3, 4), p = - \frac{6}{5}

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

p

from the center

(- 3, 4)

along the y-axis

(- 3, 4 + p)

= (- 3, 4 + (- \frac{6}{5}))

Refine

(- 3, \frac{14}{5})

x^{2} + 8 y = 0

y^{2} + 6 y + 2 x + 1 = 0

(y + 5)^{2} = - 16 (x - 3)

(x + 3)^{2} = - 12 (y + 4)

y^{2} = - 32 x