What is x^2+4y^2+2x-12y+2=0 ?

The solution to x^2+4y^2+2x-12y+2=0 is Ellipse with (h,k)=(-1, 3/2),a=2sqrt(2),b=sqrt(2)

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x^2+4y^2+2x-12y+2=0

x^{2} + 4 y^{2} + 2 x - 12 y + 2 = 0

(h, k) = (- 1, \frac{3}{2}), a = 22, b = 2

Solution steps

x^{2} + 4 y^{2} + 2 x - 12 y + 2 = 0

Rewrite

x^{2} + 4 y^{2} + 2 x - 12 y + 2 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, \frac{3}{2}), a = 22, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, \frac{3}{2}), a = 22, b = 2

\frac{( x - 5 ) ^{2}}{25} + \frac{( y + 7 ) ^{2}}{16} = 1

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

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

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{a - 16} = 1

What is x^2+4y^2+2x-12y+2=0 ?
The solution to x^2+4y^2+2x-12y+2=0 is Ellipse with (h,k)=(-1, 3/2),a=2sqrt(2),b=sqrt(2)