What is x^2+16y^2+4x-32y-44=0 ?

The solution to x^2+16y^2+4x-32y-44=0 is Ellipse with (h,k)=(-2,1),a=8,b=2

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x^2+16y^2+4x-32y-44=0

x^{2} + 16 y^{2} + 4 x - 32 y - 44 = 0

(h, k) = (- 2, 1), a = 8, b = 2

Solution steps

x^{2} + 16 y^{2} + 4 x - 32 y - 44 = 0

Rewrite

x^{2} + 16 y^{2} + 4 x - 32 y - 44 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 8, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), a = 8, b = 2

16 x^{2} + 2 y^{2} - 64 x + 150 y - 11 = 0

25 x^{2} + 16 y^{2} = 1

3 x^{2} + 7 y^{2} = 63

4 x^{2} + 32 x + 9 y^{2} + 36 y + 64 = 0

\frac{x ^{2}}{9} + \frac{( y + 5 ) ^{2}}{25} = 1

What is x^2+16y^2+4x-32y-44=0 ?
The solution to x^2+16y^2+4x-32y-44=0 is Ellipse with (h,k)=(-2,1),a=8,b=2