What is the foci x^2+9y^2-14x+36y+49=0 ?

The foci x^2+9y^2-14x+36y+49=0 is (7+4sqrt(2),-2),(7-4sqrt(2),-2)

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foci x^2+9y^2-14x+36y+49=0

foci

x^{2} + 9 y^{2} - 14 x + 36 y + 49 = 0

(7 + 42, - 2), (7 - 42, - 2)

Solution steps

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

Calculate ellipse properties

x^{2} + 9 y^{2} - 14 x + 36 y + 49 = 0 :

Ellipse with center

(h, k) = (7, - 2), a = 6, b = 2

(7 + c, - 2), (7 - c, - 2)

Compute

c :

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

(7 + 42, - 2), (7 - 42, - 2)

4 x^{2} - 24 x + \frac{y ^{2}}{16} + \frac{y}{8} + \frac{573}{16} = 0

\frac{( x + 5 ) ^{2}}{5} + \frac{( y + 9 ) ^{2}}{9} = 1

\frac{( x + 7 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{9} = 1

16 x^{2} + 9 y^{2} - 96 x + 36 y - 36 = 0

\frac{x ^{2}}{100} + \frac{y ^{2}}{44} = 1

What is the foci x^2+9y^2-14x+36y+49=0 ?
The foci x^2+9y^2-14x+36y+49=0 is (7+4sqrt(2),-2),(7-4sqrt(2),-2)