What is 2x^2+16y^2=16 ?

The solution to 2x^2+16y^2=16 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=1

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2x^2+16y^2=16

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

(h, k) = (0, 0), a = 22, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 22, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 22, b = 1

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

\frac{( ( x - 5 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{36} = 1

15 x^{2} + 10 y^{2} = 150

2 x^{2} + y^{2} - 4 x - 4 y = 0

25 x^{2} + y^{2} + 100 x + 4 y + 79 = 0

What is 2x^2+16y^2=16 ?
The solution to 2x^2+16y^2=16 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=1