What is the foci x^2-6x-5y-1=0 ?

The foci x^2-6x-5y-1=0 is (3,-3/4)

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foci x^2-6x-5y-1=0

foci

x^{2} - 6 x - 5 y - 1 = 0

(3, - \frac{3}{4})

Solution steps

Rewrite

x^{2} - 6 x - 5 y - 1 = 0

in the standard form

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

(h, k) = (3, - 2), p = \frac{5}{4}

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

p

from the center

(3, - 2)

along the y-axis

(3, - 2 + p)

= (3, - 2 + \frac{5}{4})

Refine

(3, - \frac{3}{4})

y = (x + 4)^{2}

(x + 1)^{2} = 12 (y - 3)

6 y^{2} - 12 x = 0

x^{2} - 16

(x + 1)^{2} - 2