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

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

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9x^2+14y^2=126

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{36} = 1

x^{2} + \frac{y ^{2}}{12} = 1

25 X^{2} + 4 Y^{2} - 250 X - 16 Y + 541 = 0

(\frac{x ^{2}}{169}) + (\frac{y ^{2}}{144}) = 1

- 8 y^{2} - 10 y + 72 = 9 x^{2}

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