What is the foci 9x^2-54x+y^2+2y+46=0 ?

The foci 9x^2-54x+y^2+2y+46=0 is (3,-1+4sqrt(2)),(3,-1-4sqrt(2))

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foci 9x^2-54x+y^2+2y+46=0

foci

9 x^{2} - 54 x + y^{2} + 2 y + 46 = 0

(3, - 1 + 42), (3, - 1 - 42)

Solution steps

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

Calculate ellipse properties

9 x^{2} - 54 x + y^{2} + 2 y + 46 = 0 :

Ellipse with center

(h, k) = (3, - 1), b = 6, a = 2

(3, - 1 + c), (3, - 1 - c)

Compute

c :

c = 6^{2} - 2^{2} : 42

(3, - 1 + 42), (3, - 1 - 42)

\frac{x ^{2}}{49} + \frac{y ^{2}}{4} = 1

\frac{x ^{2}}{3. 2 ^{2}} + \frac{y ^{2}}{2.4 8 ^{2}} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

5 x^{2} + 2 y^{2} = 10

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

What is the foci 9x^2-54x+y^2+2y+46=0 ?
The foci 9x^2-54x+y^2+2y+46=0 is (3,-1+4sqrt(2)),(3,-1-4sqrt(2))