What is 8x^2+2y^2-16x-16y+8=0 ?

The solution to 8x^2+2y^2-16x-16y+8=0 is Ellipse with (h,k)=(1,4),a=2,b=4

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8x^2+2y^2-16x-16y+8=0

8 x^{2} + 2 y^{2} - 16 x - 16 y + 8 = 0

(h, k) = (1, 4), a = 2, b = 4

Solution steps

8 x^{2} + 2 y^{2} - 16 x - 16 y + 8 = 0

Rewrite

8 x^{2} + 2 y^{2} - 16 x - 16 y + 8 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 4), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 4), b = 4, a = 2

12 x^{2} + 3 + 7 y^{2} = 5

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

4 x^{2} + 5 y^{2} - 32 x + 30 y - 11 = 0

\frac{( x - 4 ) ^{2}}{100} + \frac{( y + 5 ) ^{2}}{49} = 1

5 y^{2} + z^{2} = 36

What is 8x^2+2y^2-16x-16y+8=0 ?
The solution to 8x^2+2y^2-16x-16y+8=0 is Ellipse with (h,k)=(1,4),a=2,b=4