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

\frac{x ^{2}}{25} + \frac{y ^{2}}{169} = 1

9 x^{2} + 25 y^{2} = 25

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 4 ) ^{2}}{4} = 1

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

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