What is the foci-4x^2+y^2-16x-52=0 ?

The foci-4x^2+y^2-16x-52=0 is (-2,3sqrt(5)),(-2,-3sqrt(5))

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foci-4x^2+y^2-16x-52=0

foci

- 4 x^{2} + y^{2} - 16 x - 52 = 0

(- 2, 35), (- 2, - 35)

Solution steps

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

Calculate Hyperbola properties

- 4 x^{2} + y^{2} - 16 x - 52 = 0 :

Up-down Hyperbola with

(h, k) = (- 2, 0), a = 6, b = 3

(- 2, 0 + c), (- 2, 0 - c)

Compute

c :

c = 6^{2} + 3^{2} : 35

(- 2, 0 + 35), (- 2, 0 - 35)

Refine

(- 2, 35), (- 2, - 35)

\frac{y ^{2}}{9} - \frac{x ^{2}}{1} = 1

\frac{( x - 3 ) ^{2}}{16} - \frac{( y + 4 ) ^{2}}{25} = 1

4 x^{2} - 8 y^{2} = 3

\frac{y ^{2}}{1600} - \frac{x ^{2}}{5625} = 1

\frac{( x + 2 ) ^{2}}{64} - \frac{( y - 3 ) ^{2}}{36} = 1

What is the foci-4x^2+y^2-16x-52=0 ?
The foci-4x^2+y^2-16x-52=0 is (-2,3sqrt(5)),(-2,-3sqrt(5))