What is 3x^2+2y^2-6=0 ?

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

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3x^2+2y^2-6=0

3 x^{2} + 2 y^{2} - 6 = 0

(h, k) = (0, 0), a = 2, b = 3

Solution steps

3 x^{2} + 2 y^{2} - 6 = 0

Rewrite

3 x^{2} + 2 y^{2} - 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = 2

\frac{y ^{2}}{64} + \frac{x ^{2}}{100} = 1

\frac{( x + 2 ) ^{2}}{64} + \frac{( y - 3 ) ^{2}}{b} = 1

\frac{( x + 2 ) ^{2}}{4} + \frac{( y + 2 ) ^{2}}{9} = 1

\frac{( x ^{(2)} )}{( 64 )} + \frac{( y ^{(2)} )}{( 36 )} = 1

\frac{( x + 1 ) ^{2}}{\frac{15}{4}} + \frac{( y + \frac{3}{2} ) ^{2}}{16} = 1

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