What is x^2+2y^2-5=1 ?

The solution to x^2+2y^2-5=1 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(3)

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x^2+2y^2-5=1

x^{2} + 2 y^{2} - 5 = 1

(h, k) = (0, 0), a = 6, b = 3

Solution steps

x^{2} + 2 y^{2} - 5 = 1

Rewrite

x^{2} + 2 y^{2} - 5 = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = 3

\frac{x ^{2}}{841} + \frac{y ^{2}}{484} = 1

\frac{x ^{2}}{1.586 9 ^{2}} + \frac{y ^{2}}{0.9 9 ^{2}} = 1

\frac{x ^{2}}{81} + \frac{y ^{2}}{77} = 1

9 x^{2} + 18 x + 25 y^{2} + 150 y + 9 = 0

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

What is x^2+2y^2-5=1 ?
The solution to x^2+2y^2-5=1 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(3)