What is the foci 4y^2-x^2+2x+16y+7=0 ?

The foci 4y^2-x^2+2x+16y+7=0 is (1,-2+sqrt(10)),(1,-2-sqrt(10))

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foci 4y^2-x^2+2x+16y+7=0

foci

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(1, - 2 + 10), (1, - 2 - 10)

Solution steps

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

Calculate Hyperbola properties

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0 :

Up-down Hyperbola with

(h, k) = (1, - 2), a = 2, b = 22

(1, - 2 + c), (1, - 2 - c)

Compute

c :

c = 2^{2} + (22)^{2} : 10

(1, - 2 + 10), (1, - 2 - 10)

\frac{( y + 6 ) ^{2}}{36} - \frac{( x + 4 ) ^{2}}{48} = 1

9 x^{2} - 4 y^{2} - 54 x - 16 y + 29 = 0

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

\frac{y ^{2}}{16} - \frac{x ^{2}}{1} = 1

y^{2} - 2 = x^{2} - 2 x

What is the foci 4y^2-x^2+2x+16y+7=0 ?
The foci 4y^2-x^2+2x+16y+7=0 is (1,-2+sqrt(10)),(1,-2-sqrt(10))