What is x^{(2)}+4y^{(2)}+2x-12y+6=0 ?

The solution to x^{(2)}+4y^{(2)}+2x-12y+6=0 is Ellipse with (h,k)=(-1, 3/2),a=2,b=1

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x^{(2)}+4y^{(2)}+2x-12y+6=0

x^{(2)} + 4 y^{(2)} + 2 x - 12 y + 6 = 0

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

Solution steps

x^{2} + 4 y^{2} + 2 x - 12 y + 6 = 0

Rewrite

x^{2} + 4 y^{2} + 2 x - 12 y + 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

2 x - x^{2} - 4 y^{2} - 16 y - 1 > 0

\frac{x ^{2}}{36} + \frac{y ^{2}}{64} = 1

25 x^{2} + 16 y^{2} - 50 x + 64 y - 311 = 0

\frac{x ^{2}}{9} + \frac{y ^{2}}{8} = 1

\frac{( x - 1 ) ^{2}}{1} + \frac{( y - 3 ) ^{2}}{4} = 1

What is x^{(2)}+4y^{(2)}+2x-12y+6=0 ?
The solution to x^{(2)}+4y^{(2)}+2x-12y+6=0 is Ellipse with (h,k)=(-1, 3/2),a=2,b=1