What is 3x^2+y^2+12x-2y+1=0 ?

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

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3x^2+y^2+12x-2y+1=0

3 x^{2} + y^{2} + 12 x - 2 y + 1 = 0

(h, k) = (- 2, 1), a = 2, b = 23

Solution steps

3 x^{2} + y^{2} + 12 x - 2 y + 1 = 0

Rewrite

3 x^{2} + y^{2} + 12 x - 2 y + 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 2, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), b = 23, a = 2

10 y^{2} + x^{2} = 5

9 x^{2} + 4 (y - 2)^{2} = 36

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

1 x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

36 x^{2} + 9 y^{2} + 288 x - 90 y + 477 = 0

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