What is 16x^2+25y^2=1600 ?

The solution to 16x^2+25y^2=1600 is Ellipse with (h,k)=(0,0),a=10,b=8

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16x^2+25y^2=1600

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

(h, k) = (0, 0), a = 10, b = 8

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 10, b = 8

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 10, b = 8

4 x^{2} + 9 y^{2} - 8 x - 32 = 0

4 x^{2} + 9 y^{2} - 64 x + 54 y + 301 = 0

y^{2} + x^{2} - 4 y = 0

6.25 x^{2} + 16 y^{2} - 12.5 x + 64 y - 29.75 = 0

4 x^{2} + 25 y^{2} + 4 x - 120 y + 45 = 0

What is 16x^2+25y^2=1600 ?
The solution to 16x^2+25y^2=1600 is Ellipse with (h,k)=(0,0),a=10,b=8