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{8 y}{1 + x ^{2} + y ^{2}} = 2

\frac{x ^{2}}{9} + \frac{y ^{2}}{7} = 1

\frac{y ^{2}}{a ^{2}} + \frac{x ^{2}}{b ^{2}} = 1

2 x^{2} + 8 y^{2} = 50

\frac{( y - 1 ) ^{2}}{16} + \frac{( x + 3 ) ^{2}}{4} = 1

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