What is 25x^2+16y^2=400 ?

The solution to 25x^2+16y^2=400 is Ellipse with (h,k)=(0,0),a=4,b=5

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25x^2+16y^2=400

25 x^{2} + 16 y^{2} = 400

(h, k) = (0, 0), a = 4, b = 5

Solution steps

25 x^{2} + 16 y^{2} = 400

Rewrite

25 x^{2} + 16 y^{2} = 400

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 5, a = 4

\frac{x ^{2}}{9} - \frac{y ^{2}}{4} = 1

x = - \frac{1}{2} (y + 3)^{2} + 1

x^{2} + y^{2} = 121

\frac{x ^{2}}{9} + \frac{y ^{2}}{25} = 1

x^{2} = 2 y

What is 25x^2+16y^2=400 ?
The solution to 25x^2+16y^2=400 is Ellipse with (h,k)=(0,0),a=4,b=5