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

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

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

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

(h, k) = (- 6, 0), a = 6, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - 6 ) ) ^{2}}{6 ^{2}} + \frac{( y - 0 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 6, 0), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 6, 0), a = 6, b = 3

\frac{( x - 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{25} + \frac{( y + 2 ) ^{2}}{49} = 1

16 x^{2} + y^{2} + 96 x - 10 y = - 153

x^{2} + y^{2} - 25 = \frac{x + 25}{7} - y

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 2 ) ^{2}}{25} = 1

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