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

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

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

foci

(h + a^{2} - b^{2}, k), (h - a^{2} - b^{2}, k)

Solution steps

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

Calculate ellipse properties

\frac{( x - h ) ^{2}}{a ^{2}} + \frac{( y - k ) ^{2}}{b ^{2}} = 1 :

Ellipse with center

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

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

Compute

c :

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

(h + a^{2} - b^{2}, k), (h - a^{2} - b^{2}, k)

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