What is 4x^2+8y^2-16*+32y+32=0 ?

The solution to 4x^2+8y^2-16*+32y+32=0 is Ellipse with (h,k)=(0,-2),a=2,b=sqrt(2)

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4x^2+8y^2-16*+32y+32=0

4 x^{2} + 8 y^{2} - 16 \cdot + 32 y + 32 = 0

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

Solution steps

4 x^{2} + 8 y^{2} - 16 + 32 y + 32 = 0

Rewrite

4 x^{2} + 8 y^{2} - 16 + 32 y + 32 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{6} + \frac{y ^{2}}{2} = 1

y^{2} = \frac{4 - x ^{2}}{5}

\frac{( x + 4 ) ^{2}}{64} + \frac{( y + 2 ) ^{2}}{100} = 1

490 x^{(2)} + 10 y^{(2)} + 808 x - 556 y + 40 = 0

16 X^{2} + 25 Y^{2} - 64 X - 50 Y - 311 = 0

What is 4x^2+8y^2-16*+32y+32=0 ?
The solution to 4x^2+8y^2-16*+32y+32=0 is Ellipse with (h,k)=(0,-2),a=2,b=sqrt(2)