What is (3-y^2-3x^2)=0 ?

The solution to (3-y^2-3x^2)=0 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(3)

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(3-y^2-3x^2)=0

(3 - y^{2} - 3 x^{2}) = 0

(h, k) = (0, 0), a = 1, b = 3

Solution steps

(3 - y^{2} - 3 x^{2}) = 0

Rewrite

(3 - y^{2} - 3 x^{2}) = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, 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 = 1

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 7 ) ^{2}}{36} = 1

\frac{( ( x - 2 ) ^{2} )}{( 9 )} + \frac{( ( y + 5 ) ^{2} )}{( 25 )} = 1

16 x^{2} + 25 y^{2} = 1400

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

(\frac{x}{16})^{2} + \frac{y ^{2}}{81} = 1

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