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

The solution to x^2+4y^2-4x-32y+32=0 is Ellipse with (h,k)=(2,4),a=6,b=3

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

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

(h, k) = (2, 4), a = 6, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{6 ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 4), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 4), a = 6, b = 3

\frac{( x - 1 ) ^{2}}{5} + \frac{( y + 2 ) ^{2}}{8} = 1

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

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

\frac{x ^{2}}{6} + \frac{y ^{2}}{25} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{81} = 1

What is x^2+4y^2-4x-32y+32=0 ?
The solution to x^2+4y^2-4x-32y+32=0 is Ellipse with (h,k)=(2,4),a=6,b=3