What is the foci y^2-6y-2x+7=0 ?

The foci y^2-6y-2x+7=0 is (-1/2 ,3)

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foci y^2-6y-2x+7=0

foci

y^{2} - 6 y - 2 x + 7 = 0

(- \frac{1}{2}, 3)

Solution steps

Rewrite

y^{2} - 6 y - 2 x + 7 = 0

in the standard form

4 \cdot \frac{1}{2} (x - (- 1)) = (y - 3)^{2}

(h, k) = (- 1, 3), p = \frac{1}{2}

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

p

from the center

(- 1, 3)

along the x-axis

(- 1 + p, 3)

= (- 1 + \frac{1}{2}, 3)

Refine

(- \frac{1}{2}, 3)

y = - 0.0000848 x^{2} - 0.006005 x + 1.004

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

40 x - 5 x^{2}

x = - \frac{3}{8} (y - 2)^{2} - 1

y = 3 x^{2} - 7