What is the foci 36x^2-4y^2-216x+16y+452=0 ?

The foci 36x^2-4y^2-216x+16y+452=0 is (3,2+2sqrt(10)),(3,2-2sqrt(10))

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foci 36x^2-4y^2-216x+16y+452=0

foci

36 x^{2} - 4 y^{2} - 216 x + 16 y + 452 = 0

(3, 2 + 210), (3, 2 - 210)

Solution steps

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

Calculate Hyperbola properties

36 x^{2} - 4 y^{2} - 216 x + 16 y + 452 = 0 :

Up-down Hyperbola with

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

(3, 2 + c), (3, 2 - c)

Compute

c :

c = 6^{2} + 2^{2} : 210

(3, 2 + 210), (3, 2 - 210)

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

\frac{y ^{2}}{25} - \frac{( x + 3 ) ^{2}}{56} = 1

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

25 x^{2} - 9 y^{2} = 225

\frac{( y - 5 ) ^{2}}{16} - \frac{( x - 4 ) ^{2}}{9} = 1

What is the foci 36x^2-4y^2-216x+16y+452=0 ?
The foci 36x^2-4y^2-216x+16y+452=0 is (3,2+2sqrt(10)),(3,2-2sqrt(10))