What is x^2+3y^2=28 ?

The solution to x^2+3y^2=28 is Ellipse with (h,k)=(0,0),a=2sqrt(7),b=(2sqrt(7))/(sqrt(3))

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x^2+3y^2=28

x^{2} + 3 y^{2} = 28

(h, k) = (0, 0), a = 27, b = \frac{2 7}{3}

Solution steps

x^{2} + 3 y^{2} = 28

Rewrite

x^{2} + 3 y^{2} = 28

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 7 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2 7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 27, b = \frac{2 7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 27, b = \frac{2 7}{3}

12 x^{2} + 3 y^{2} + 12 y - 96 = 0

\frac{( x - 3 ) ^{2}}{2} + (y + 5)^{2} = 8

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

9 x^{2} + 25 y^{2} = 64

What is x^2+3y^2=28 ?
The solution to x^2+3y^2=28 is Ellipse with (h,k)=(0,0),a=2sqrt(7),b=(2sqrt(7))/(sqrt(3))