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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{( x - 1 ) ^{2}}{25} + \frac{( y - 1 ) ^{2}}{3} = 1

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

\frac{( x - 0 ) ^{2}}{25} + \frac{( y - 0 ) ^{2}}{2.25} = 1

\frac{( x - 5 ) ^{2}}{49} + \frac{( y - 8 ) ^{2}}{11} = 1

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