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

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

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

foci

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

(0, - 1 + 5), (0, - 1 - 5)

Solution steps

(h, k + c), (h, k - c)

Calculate Hyperbola properties

y^{2} + 2 y = 4 x^{2} + 3 :

Up-down Hyperbola with

(h, k) = (0, - 1), a = 2, b = 1

(0, - 1 + c), (0, - 1 - c)

Compute

c :

c = 2^{2} + 1^{2} : 5

(0, - 1 + 5), (0, - 1 - 5)

9 x^{2} - 4 y^{2} - 18 x + 16 y - 43 = 0

\frac{x ^{2}}{36} - \frac{y ^{2}}{81} = 1

\frac{x ^{2}}{100} - \frac{y ^{2}}{36} = 1

4 x^{2} - 9 y^{2} + 32 x + 36 y + 64 = 0

\frac{y ^{2}}{36} - \frac{x ^{2}}{49} = 1

What is the foci y^2+2y=4x^2+3 ?
The foci y^2+2y=4x^2+3 is (0,-1+sqrt(5)),(0,-1-sqrt(5))