What is the foci (x^2)/(a^2)+(y^2)/(b^2)=1 ?

The foci (x^2)/(a^2)+(y^2)/(b^2)=1 is (sqrt(a^2-b^2),0),(-sqrt(a^2-b^2),0)

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foci (x^2)/(a^2)+(y^2)/(b^2)=1

foci

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1

(a^{2} - b^{2}, 0), (- a^{2} - b^{2}, 0)

Solution steps

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

Calculate ellipse properties

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 :

Ellipse with center

(h, k) = (0, 0), a = a, b = b

(0 + c, 0), (0 - c, 0)

Compute

c :

c = a^{2} - b^{2}

(0 + a^{2} - b^{2}, 0), (0 - a^{2} - b^{2}, 0)

Refine

(a^{2} - b^{2}, 0), (- a^{2} - b^{2}, 0)

\frac{( x ^{2} )}{16} + \frac{( y ^{2} )}{36} = 1

x^{2} + 4 y^{2} + 10 x + 8 y - 3 = 0

36 x^{2} + y^{2} = 36

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

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