What is x^2+4y^2+20x+44y+121=0 ?

The solution to x^2+4y^2+20x+44y+121=0 is Ellipse with (h,k)=(-10,-11/2),a=10,b=5

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x^2+4y^2+20x+44y+121=0

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

(h, k) = (- 10, - \frac{11}{2}), a = 10, b = 5

Solution steps

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

Rewrite

x^{2} + 4 y^{2} + 20 x + 44 y + 121 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 10 ) ) ^{2}}{1 0 ^{2}} + \frac{( y - ( - \frac{11}{2} ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 10, - \frac{11}{2}), a = 10, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 10, - \frac{11}{2}), a = 10, b = 5

16 x^{2} + 7 y^{2} = 112

\frac{( x + 1 ) ^{2}}{2} + \frac{y ^{2}}{8} = 1

y^{2} = - 0.25 x^{2} + 1

x, \frac{x ^{2}}{25} + \frac{Y ( x ) ^{2}}{4} = 1

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1

What is x^2+4y^2+20x+44y+121=0 ?
The solution to x^2+4y^2+20x+44y+121=0 is Ellipse with (h,k)=(-10,-11/2),a=10,b=5