What is 0= 1/2 x^2-1+1/4 y^2 ?

The solution to 0= 1/2 x^2-1+1/4 y^2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2

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0= 1/2 x^2-1+1/4 y^2

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

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

Solution steps

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

Rewrite

0 - \frac{1}{2} x^{2} + 1 - \frac{1}{4} y^{2} = 0

in the form of the standard ellipse equation

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

4 x^{(2)} + 9 y^{(2)} = 36

\frac{( x - 2 ) ^{2}}{36} + \frac{( y - 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{64} + \frac{y ^{2}}{81} = 1

4 y^{2} + 3 x^{2} = 48

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

What is 0= 1/2 x^2-1+1/4 y^2 ?
The solution to 0= 1/2 x^2-1+1/4 y^2 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2