What is the foci y^2+2y+1=-2x+4 ?

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

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foci y^2+2y+1=-2x+4

foci

y^{2} + 2 y + 1 = - 2 x + 4

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

Solution steps

Rewrite

y^{2} + 2 y + 1 = - 2 x + 4

in the standard form

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

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

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

p

from the center

(2, - 1)

along the x-axis

(2 + p, - 1)

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

Refine

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

(y - 3)^{2} = - 8 (x + 2)

y = + x^{2} + 6 x

y = - x^{2} + 14 x + 49

2 x^{2} - 4 x + 15

x^{2} - 4 x + 5