What is x^2+4y^2-80y+396=0 ?

The solution to x^2+4y^2-80y+396=0 is Ellipse with (h,k)=(0,10),a=2,b=1

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x^2+4y^2-80y+396=0

x^{2} + 4 y^{2} - 80 y + 396 = 0

(h, k) = (0, 10), a = 2, b = 1

Solution steps

x^{2} + 4 y^{2} - 80 y + 396 = 0

Rewrite

x^{2} + 4 y^{2} - 80 y + 396 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 10), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 10), a = 2, b = 1

25 x^{2} + 144 y^{2} = 900

\frac{( x + 5 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{4} = 1

4 x^{2} + 16 y^{2} - 8 x + 32 y - 44 = 0

16 - x^{2} - 4 y^{2} \geq 0

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

What is x^2+4y^2-80y+396=0 ?
The solution to x^2+4y^2-80y+396=0 is Ellipse with (h,k)=(0,10),a=2,b=1