What is 25x^{(2)}+4y^{(2)}=100 ?

The solution to 25x^{(2)}+4y^{(2)}=100 is Ellipse with (h,k)=(0,0),a=2,b=5

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25x^{(2)}+4y^{(2)}=100

25 x^{(2)} + 4 y^{(2)} = 100

(h, k) = (0, 0), a = 2, b = 5

Solution steps

25 x^{2} + 4 y^{2} = 100

Rewrite

25 x^{2} + 4 y^{2} = 100

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, 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 = 2

x^{2} 64 + y^{2} 49 = 1

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

\frac{( x + 1 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{25} = 1

\frac{x ^{2}}{256} + \frac{y ^{2}}{400} = 1

\frac{( x - 1 ) ^{2}}{13} + \frac{( y + 5 ) ^{2}}{12} = 1

What is 25x^{(2)}+4y^{(2)}=100 ?
The solution to 25x^{(2)}+4y^{(2)}=100 is Ellipse with (h,k)=(0,0),a=2,b=5