What is 4x^2+y^2+8x+2y-31=0 ?

The solution to 4x^2+y^2+8x+2y-31=0 is Ellipse with (h,k)=(-1,-1),a=3,b=6

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4x^2+y^2+8x+2y-31=0

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

(h, k) = (- 1, - 1), a = 3, b = 6

Solution steps

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

Rewrite

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, - 1), a = 3, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, - 1), b = 6, a = 3

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

x^{2} + 4 y^{2} - 6 x - 55 = 0

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

(\frac{x - 2}{4})^{2} + (\frac{y + 3}{16})^{2} = 1

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 3 ) ^{2}}{4} = 1

What is 4x^2+y^2+8x+2y-31=0 ?
The solution to 4x^2+y^2+8x+2y-31=0 is Ellipse with (h,k)=(-1,-1),a=3,b=6