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

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

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

foci

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

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

Solution steps

Rewrite

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

in the standard form

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

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

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

p

from the center

(1, - 1)

along the y-axis

(1, - 1 + p)

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

Refine

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

81 y^{2}

- x^{2} + 10 x - 5

16 t^{2} + 48 t + 4

- 0.4 x^{2} - 5

x^{2} + 6 x = 4 y - 5