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

The solution to x^2-4x+16y^2+32y+4=0 is Ellipse with (h,k)=(2,-1),a=4,b=1

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 12 y^{2} = 108

x^{2} + 3 y^{2} + 4 x + 18 y + 22 = 0

36 x^{2} - 36 x + 64 y^{2} + 256 y + 265 = 576

x^{2} + y^{2} - 14 y = 0

\frac{x ^{2}}{( 2.67 ) ^{2}} + \frac{y ^{2}}{( 2.85 ) ^{2}} = 1

What is x^2-4x+16y^2+32y+4=0 ?
The solution to x^2-4x+16y^2+32y+4=0 is Ellipse with (h,k)=(2,-1),a=4,b=1