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

The foci y^2-4x^2<1 is (0,(sqrt(5))/2),(0,-(sqrt(5))/2)

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foci y^2-4x^2<1

foci

y^{2} - 4 x^{2} < 1

(0, \frac{5}{2}), (0, - \frac{5}{2})

Solution steps

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

Rewrite as

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

Calculate Hyperbola properties

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

Up-down Hyperbola with

(h, k) = (0, 0), a = 1, b = \frac{1}{2}

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

Compute

c :

c = 1^{2} + (\frac{1}{2})^{2} : \frac{5}{2}

(0, 0 + \frac{5}{2}), (0, 0 - \frac{5}{2})

Refine

(0, \frac{5}{2}), (0, - \frac{5}{2})

x^{2} - 16 y^{2} = 64

(\frac{( x ^{2} )}{27}) - \frac{( ( y ) ^{2} )}{36} = 1

x^{2} - y^{2} - 6 x + 16 y - 119 = 0

9 x^{2} - 25 y^{2} = 900

(\frac{x - 5}{8})^{2} - (\frac{y + 2}{7})^{2} = 1

What is the foci y^2-4x^2<1 ?
The foci y^2-4x^2<1 is (0,(sqrt(5))/2),(0,-(sqrt(5))/2)