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

The solution to x^2-4x+4y^2-16y-4=0 is Ellipse with (h,k)=(2,2),a=2sqrt(6),b=sqrt(6)

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

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

(h, k) = (2, 2), a = 26, b = 6

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 2), a = 26, b = 6

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, 2), a = 26, b = 6

9 x^{2} + 4 y^{2} + 42 x - 54 y - 49 = 0

2 z^{2} - 2 z + 1 + y^{2} = 1

2 x^{2} + y^{2} + 6 x - 2 y - 10 = 0

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

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

What is x^2-4x+4y^2-16y-4=0 ?
The solution to x^2-4x+4y^2-16y-4=0 is Ellipse with (h,k)=(2,2),a=2sqrt(6),b=sqrt(6)