What is the foci x^2-4x-y+3=0 ?

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

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foci x^2-4x-y+3=0

foci

x^{2} - 4 x - y + 3 = 0

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

Solution steps

Rewrite

x^{2} - 4 x - y + 3 = 0

in the standard form

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

(h, k) = (2, - 1), p = \frac{1}{4}

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

p

from the center

(2, - 1)

along the y-axis

(2, - 1 + p)

= (2, - 1 + \frac{1}{4})

Refine

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

- 2 x^{2} + 24 x + y - 70 = 0

y = - 4 x^{2} + 1

x^{2} - 20 y - 2 x - 39 = 0

y^{2} + x + y = 0

y = (x + 1) (x + 2)