What is x^2+4y^2-2x+16y+1=0 ?

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

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x^2+4y^2-2x+16y+1=0

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

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

Solution steps

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

Rewrite

x^{2} + 4 y^{2} - 2 x + 16 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{( x - 4 ) ^{2}}{36} + \frac{y ^{2}}{20} = 1

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

\frac{x ^{2}}{7} + \frac{y ^{2}}{5} = 1

\frac{( x + 6 ) ^{2}}{100} + \frac{( y - 8 ) ^{2}}{36} = 1

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