What is 12x^2+y^2=24 ?

The solution to 12x^2+y^2=24 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2sqrt(6)

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12x^2+y^2=24

12 x^{2} + y^{2} = 24

(h, k) = (0, 0), a = 2, b = 26

Solution steps

12 x^{2} + y^{2} = 24

Rewrite

12 x^{2} + y^{2} = 24

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 26

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 26, a = 2

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

36 x^{2} + 16 y^{2} = 576

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

3 x^{2} + 2 y^{2} \leq 13950

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

What is 12x^2+y^2=24 ?
The solution to 12x^2+y^2=24 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2sqrt(6)