x^2+6y^2=3

Solution

x^{2} + 6 y^{2} = 3

(h, k) = (0, 0), a = 3, b = \frac{1}{2}

Solution steps

x^{2} + 6 y^{2} = 3

Rewrite

x^{2} + 6 y^{2} = 3

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = \frac{1}{2}

\frac{( x + 6 ) ^{2}}{18} + \frac{( y + 3 ) ^{2}}{9} = 1

3 x^{2} + 3 y^{2} - 36 y = 0

4 x^{2} + 8 y^{2} - 4 x - 24 y - 13 = 0

x^{2} + 16 y^{2} - 2 x - 64 y + 49 = 0

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

What is x^2+6y^2=3 ?
The solution to x^2+6y^2=3 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(1/2)