What is the foci x^2=-6(y-7) ?

The foci x^2=-6(y-7) is (0, 11/2)

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foci x^2=-6(y-7)

foci

x^{2} = - 6 (y - 7)

(0, \frac{11}{2})

Solution steps

Rewrite

x^{2} = - 6 (y - 7)

in the standard form:

4 (- \frac{3}{2}) (y - 7) = (x - 0)^{2}

(h, k) = (0, 7), p = - \frac{3}{2}

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

p

from the center

(0, 7)

along the y-axis

(0, 7 + p)

= (0, 7 + (- \frac{3}{2}))

Refine

(0, \frac{11}{2})

2 y^{2} = 16 x

x^{2} + 2 x

x = + (y + 1)^{2} - 9

- 3 x^{2} + 8 x + 896

x^{2} + 36