What is (2x+4y)^2=16xy+16 ?

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

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(2x+4y)^2=16xy+16

(2 x + 4 y)^{2} = 16 x y + 16

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

Solution steps

(2 x + 4 y)^{2} = 16 x y + 16

Rewrite

(2 x + 4 y)^{2} - 16 x y - 16 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{9} + \frac{y ^{2}}{4} = 2

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

2 x^{2} + 4 y^{2} + 14 x + 8 y + 16 = 0

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

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