What is 220x^2+256y^2-660x-3025=0 ?

The solution to 220x^2+256y^2-660x-3025=0 is Ellipse with (h,k)=(3/2 ,0),a=4,b=(sqrt(55))/2

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220x^2+256y^2-660x-3025=0

220 x^{2} + 256 y^{2} - 660 x - 3025 = 0

(h, k) = (\frac{3}{2}, 0), a = 4, b = \frac{55}{2}

Solution steps

220 x^{2} + 256 y^{2} - 660 x - 3025 = 0

Rewrite

220 x^{2} + 256 y^{2} - 660 x - 3025 = 0

in the form of the standard ellipse equation

\frac{( x - \frac{3}{2} ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{55}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{3}{2}, 0), a = 4, b = \frac{55}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{3}{2}, 0), a = 4, b = \frac{55}{2}

x^{2} + y^{2} + 12 y^{2} - 108 = 0

4 x^{2} + 8 y^{2} = 16

x^{2} + 4 y^{2} - 6 x - 32 y + 72 = 0

(- y^{2}) = x^{2} + 12

\frac{( x - 3 ) ^{2}}{9} + \frac{( y + 1 ) ^{2}}{16} = 1

What is 220x^2+256y^2-660x-3025=0 ?
The solution to 220x^2+256y^2-660x-3025=0 is Ellipse with (h,k)=(3/2 ,0),a=4,b=(sqrt(55))/2