What is the foci ((x-7)^2)/(81)+((y-6)^2)/(64)=1 ?

The foci ((x-7)^2)/(81)+((y-6)^2)/(64)=1 is (7+sqrt(17),6),(7-sqrt(17),6)

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foci ((x-7)^2)/(81)+((y-6)^2)/(64)=1

foci

\frac{( x - 7 ) ^{2}}{81} + \frac{( y - 6 ) ^{2}}{64} = 1

(7 + 17, 6), (7 - 17, 6)

Solution steps

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

Calculate ellipse properties

\frac{( x - 7 ) ^{2}}{81} + \frac{( y - 6 ) ^{2}}{64} = 1 :

Ellipse with center

(h, k) = (7, 6), a = 9, b = 8

(7 + c, 6), (7 - c, 6)

Compute

c :

c = 9^{2} - 8^{2} : 17

(7 + 17, 6), (7 - 17, 6)

\frac{( X + 3 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

6 x^{2} + 10 y^{2} = 60

4 x^{2} + 9 y^{2} + 24 x - 90 y = - 225

\frac{x ^{2}}{36} + \frac{y ^{2}}{20} = 1

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

What is the foci ((x-7)^2)/(81)+((y-6)^2)/(64)=1 ?
The foci ((x-7)^2)/(81)+((y-6)^2)/(64)=1 is (7+sqrt(17),6),(7-sqrt(17),6)