What is 3x^2+z^2=8-x^2-z^2 ?

The solution to 3x^2+z^2=8-x^2-z^2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2

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3x^2+z^2=8-x^2-z^2

3 x^{2} + z^{2} = 8 - x^{2} - z^{2}

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

Solution steps

3 x^{2} + z^{2} = 8 - x^{2} - z^{2}

Rewrite

3 x^{2} + z^{2} - 8 + x^{2} + z^{2} = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

- \frac{x ^{2}}{1} - \frac{y ^{2}}{4} = 1

\frac{( x + 2 ) ^{2}}{25} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{x ^{2}}{14} + \frac{y ^{2}}{6} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{c} = 1

16 x^{2} + 36 y^{2} - 256 x + 448 = 0

What is 3x^2+z^2=8-x^2-z^2 ?
The solution to 3x^2+z^2=8-x^2-z^2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2