What is 6x^2+y^2+12x=0 ?

The solution to 6x^2+y^2+12x=0 is Ellipse with (h,k)=(-1,0),a=1,b=sqrt(6)

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6x^2+y^2+12x=0

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

(h, k) = (- 1, 0), a = 1, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 0), a = 1, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 0), b = 6, a = 1

2 - \frac{2 - 2 x}{2 x - x ^{2} - y ^{2}} = 0

(\frac{x ^{2}}{64}) + (\frac{y ^{2}}{36}) = 1

X^{2} + 2 \cdot Y^{2} - 2 \cdot X - 4 \cdot Y - 8 = 0

\frac{x ^{2}}{21} + \frac{y ^{2}}{25} = 1

4 x^{2} + 16 y^{2} + 16 x + 160 y + 352 = 0

What is 6x^2+y^2+12x=0 ?
The solution to 6x^2+y^2+12x=0 is Ellipse with (h,k)=(-1,0),a=1,b=sqrt(6)