What is the foci y^2-8x-6y-3=0 ?

The foci y^2-8x-6y-3=0 is (1/2 ,3)

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foci y^2-8x-6y-3=0

foci

y^{2} - 8 x - 6 y - 3 = 0

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

Solution steps

Rewrite

y^{2} - 8 x - 6 y - 3 = 0

in the standard form

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

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

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

p

from the center

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

along the x-axis

(- \frac{3}{2} + p, 3)

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

Refine

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

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

x = 3 - 5 (y + 1)^{2}

y = x^{2} - 6 x + 11

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

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