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

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

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

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

(h, k) = (- 2, 0), a = 4, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, 0), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 0), a = 4, b = 2

12 x^{2} + 5 y^{2} - 60 = 0

9 x^{2} + 16 y^{2} + 96 y - 36 x + 36 = 0

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

4 x^{2} + 16 y^{2} - 64 = 1

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

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