What is 14x^2+9y^2=126 ?

The solution to 14x^2+9y^2=126 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(14)

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14x^2+9y^2=126

14 x^{2} + 9 y^{2} = 126

(h, k) = (0, 0), a = 3, b = 14

Solution steps

14 x^{2} + 9 y^{2} = 126

Rewrite

14 x^{2} + 9 y^{2} = 126

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{( 14 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 14

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 14, a = 3

3 x^{2} + 2 y^{2} - 18 = 0

3 x^{2} + 4 y^{2} = \frac{1}{2}

5 x^{2} + 9 y^{2} - 10 x + 4 = 0

3 x^{(2)} + y^{(2)} - 24 x + 39 = 0

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

What is 14x^2+9y^2=126 ?
The solution to 14x^2+9y^2=126 is Ellipse with (h,k)=(0,0),a=3,b=sqrt(14)