What is 25x^2+64y^2-400x-640y+1600=0 ?

The solution to 25x^2+64y^2-400x-640y+1600=0 is Ellipse with (h,k)=(8,5),a=8,b=5

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25x^2+64y^2-400x-640y+1600=0

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

(h, k) = (8, 5), a = 8, b = 5

Solution steps

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

Rewrite

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{8 ^{2}} + \frac{( y - 5 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, 5), a = 8, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, 5), a = 8, b = 5

What is 25x^2+64y^2-400x-640y+1600=0 ?
The solution to 25x^2+64y^2-400x-640y+1600=0 is Ellipse with (h,k)=(8,5),a=8,b=5