What is x^2+3y^2+2x-12y+10=0 ?

The solution to x^2+3y^2+2x-12y+10=0 is Ellipse with (h,k)=(-1,2),a=sqrt(3),b=1

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x^2+3y^2+2x-12y+10=0

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

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

Solution steps

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

Rewrite

x^{2} + 3 y^{2} + 2 x - 12 y + 10 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 8 y^{2} + 6 x + 10 y - 12 = 0

4 x^{2} + 9 y^{2} - 32 x - 36 y + 64 = 0

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

25 x^{2} + 16 y^{2} + 100 x - 96 y - 156 = 0

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

What is x^2+3y^2+2x-12y+10=0 ?
The solution to x^2+3y^2+2x-12y+10=0 is Ellipse with (h,k)=(-1,2),a=sqrt(3),b=1