What is 8x^2+2y^2-32=0 ?

The solution to 8x^2+2y^2-32=0 is Ellipse with (h,k)=(0,0),a=2,b=4

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8x^2+2y^2-32=0

8 x^{2} + 2 y^{2} - 32 = 0

(h, k) = (0, 0), a = 2, b = 4

Solution steps

8 x^{2} + 2 y^{2} - 32 = 0

Rewrite

8 x^{2} + 2 y^{2} - 32 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 4, a = 2

\frac{( x - 3 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{9} = 1

16 x^{2} + 25 y^{2} - 96 x - 250 y + 369 = 0

9 (x + 4)^{2} + 13 (y - 1)^{2} = 117

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

x^{2} + 2 x + 4 y^{2} - 12 y + 7 = 0

What is 8x^2+2y^2-32=0 ?
The solution to 8x^2+2y^2-32=0 is Ellipse with (h,k)=(0,0),a=2,b=4