What is 100x^2+9y^2=900 ?

The solution to 100x^2+9y^2=900 is Ellipse with (h,k)=(0,0),a=3,b=10

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100x^2+9y^2=900

100 x^{2} + 9 y^{2} = 900

(h, k) = (0, 0), a = 3, b = 10

Solution steps

100 x^{2} + 9 y^{2} = 900

Rewrite

100 x^{2} + 9 y^{2} = 900

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{1 0 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 10

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 10, a = 3

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

\frac{( x - 2 ) ^{2}}{49} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 4 y^{2} - 225 = 0

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

\frac{( x - 1 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{5100} = 1

What is 100x^2+9y^2=900 ?
The solution to 100x^2+9y^2=900 is Ellipse with (h,k)=(0,0),a=3,b=10