What is the foci-4/3+2x+x^2+(4y)/3+(y^2)/3 =0 ?

The foci-4/3+2x+x^2+(4y)/3+(y^2)/3 =0 is (-1,-2+sqrt(22/3)),(-1,-2-sqrt(22/3))

Popular >

foci-4/3+2x+x^2+(4y)/3+(y^2)/3 =0

foci

- \frac{4}{3} + 2 x + x^{2} + \frac{4 y}{3} + \frac{y ^{2}}{3} = 0

(- 1, - 2 + \frac{22}{3}), (- 1, - 2 - \frac{22}{3})

Solution steps

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

Calculate ellipse properties

- \frac{4}{3} + 2 x + x^{2} + \frac{4 y}{3} + \frac{y ^{2}}{3} = 0 :

Ellipse with center

(h, k) = (- 1, - 2), b = 11, a = \frac{11}{3}

(- 1, - 2 + c), (- 1, - 2 - c)

Compute

c :

c = 11^{2} - \frac{11}{3}^{2} : \frac{22}{3}

(- 1, - 2 + \frac{22}{3}), (- 1, - 2 - \frac{22}{3})

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

\frac{( x - 1 ) ^{2}}{8} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{20} = 1

\frac{( x 8 ) ^{2}}{49} + \frac{( y + 1 ) ^{2}}{100} = 1

\frac{x ^{2}}{32} + \frac{y ^{2}}{18} = 1

What is the foci-4/3+2x+x^2+(4y)/3+(y^2)/3 =0 ?
The foci-4/3+2x+x^2+(4y)/3+(y^2)/3 =0 is (-1,-2+sqrt(22/3)),(-1,-2-sqrt(22/3))