What is 25x^2+64y^2=1600 ?

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

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25x^2+64y^2=1600

25 x^{2} + 64 y^{2} = 1600

(h, k) = (0, 0), a = 8, b = 5

Solution steps

25 x^{2} + 64 y^{2} = 1600

Rewrite

25 x^{2} + 64 y^{2} = 1600

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{8 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 8, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 8, b = 5

\frac{( x + 4 ) ^{2}}{9} + \frac{( y - 6 ) ^{2}}{25} = 1

\frac{( y - 8 ) ^{2}}{40} + \frac{( x + 10 ) ^{2}}{211} = 1

4 y^{2} + 16 x^{2} - 36 x - 20 y + 36 = 0

\frac{x ^{2}}{25} + \frac{y ^{2}}{76} = 1

x^{2} + 4 y^{2} = - 4 x

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