What is 16x^{(2)}+25y^{(2)}=400 ?

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

16 x^{2} - 160 x + 25 y^{2} + 350 y - 1225 = 0

9 x^{2} + 16 y^{2} - 18 x - 64 y = 71

21 y^{2} + 210 y + 25 x^{2} - 100 x = 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{16} = 1

(\frac{x - 1}{2})^{2} + (y + 3)^{2} = \frac{49}{64}

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