What is 2x^{(2)}+y^{(2)}=1 ?

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

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2x^{(2)}+y^{(2)}=1

2 x^{(2)} + y^{(2)} = 1

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1, a = \frac{1}{2}

16 - x^{2} - 9 y^{2} = - 1

y^{2} = 100 - 4 x^{2}

4 x^{2} + y^{2} + 4 x + 8 y + 12 = 0

\frac{( x - 3 ) ^{2}}{18} + \frac{( y + 4 ) ^{2}}{32} = 1

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

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