What is x^2+3y^2-4x+12y+13=0 ?

The solution to x^2+3y^2-4x+12y+13=0 is Ellipse with (h,k)=(2,-2),a=sqrt(3),b=1

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x^2+3y^2-4x+12y+13=0

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

(h, k) = (2, - 2), a = 3, b = 1

Solution steps

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

Rewrite

x^{2} + 3 y^{2} - 4 x + 12 y + 13 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 2), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 2), a = 3, b = 1

4 x^{2} + 3 y^{2} - 32 x - 18 y + 43 = 0

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

100 x^{2} + 64 y^{2} < 1600

9 x^{2} + 4 y^{2} + 90 x + 8 y + 193 = 0

25 x^{2} + 9 y^{2} + 50 x - 108 y + 124 = 0

What is x^2+3y^2-4x+12y+13=0 ?
The solution to x^2+3y^2-4x+12y+13=0 is Ellipse with (h,k)=(2,-2),a=sqrt(3),b=1