What is 4x^2+y^2+4x+8y+12=0 ?

The solution to 4x^2+y^2+4x+8y+12=0 is Ellipse with (h,k)=(-1/2 ,-4),a=(sqrt(5))/2 ,b=sqrt(5)

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4x^2+y^2+4x+8y+12=0

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

(h, k) = (- \frac{1}{2}, - 4), a = \frac{5}{2}, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{2}, - 4), a = \frac{5}{2}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{2}, - 4), b = 5, a = \frac{5}{2}

\frac{( x - 3 ) ^{2}}{18} + \frac{( y + 4 ) ^{2}}{32} = 1

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

\frac{x ^{2}}{85} + \frac{y ^{2}}{4} = 1

x, \frac{x ^{2}}{16} + \frac{Y ( x ) ^{2}}{4} = 1

\frac{x ^{2} - 2 x + y ^{2}}{4 - y} = 14

What is 4x^2+y^2+4x+8y+12=0 ?
The solution to 4x^2+y^2+4x+8y+12=0 is Ellipse with (h,k)=(-1/2 ,-4),a=(sqrt(5))/2 ,b=sqrt(5)