What is the foci 18x^2+4y^2-72x+4y+37=0 ?

The foci 18x^2+4y^2-72x+4y+37=0 is (2,(-1+2sqrt(7))/2),(2,(-1-2sqrt(7))/2)

Popular >

foci 18x^2+4y^2-72x+4y+37=0

foci

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0

(2, \frac{- 1 + 2 7}{2}), (2, \frac{- 1 - 2 7}{2})

Solution steps

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

Calculate ellipse properties

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0 :

Ellipse with center

(h, k) = (2, - \frac{1}{2}), b = 3, a = 2

(2, - \frac{1}{2} + c), (2, - \frac{1}{2} - c)

Compute

c :

c = 3^{2} - 2^{2} : 7

(2, - \frac{1}{2} + 7), (2, - \frac{1}{2} - 7)

Refine

(2, \frac{- 1 + 2 7}{2}), (2, \frac{- 1 - 2 7}{2})

16 x^{2} + 25 y^{2} + 64 x - 200 y + 64 = 0

\frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

\frac{( y + 3 ) ^{2}}{144} + \frac{( x + 2 ) ^{2}}{25} = 1

5 x^{2} + 9 y^{2} - 20 x + 54 y + 56 = 0

25 x^{2} + 4 y^{2} - 250 x - 16 y + 541 = 0

What is the foci 18x^2+4y^2-72x+4y+37=0 ?
The foci 18x^2+4y^2-72x+4y+37=0 is (2,(-1+2sqrt(7))/2),(2,(-1-2sqrt(7))/2)