What is 4x^2+16x+16y^2-32y-32=0 ?

The solution to 4x^2+16x+16y^2-32y-32=0 is Ellipse with (h,k)=(-2,1),a=4,b=2

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4x^2+16x+16y^2-32y-32=0

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

(h, k) = (- 2, 1), a = 4, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = 4, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), a = 4, b = 2

\frac{( x ^{(2)} )}{( 16 )} + \frac{( y ^{(2)} )}{( 7 )} = 1

\frac{( x - 4 ) ^{2}}{5 ^{2}} + \frac{( y - 7 ) ^{2}}{3 ^{2}} = 1

9 x^{2} + 25 y^{2} + 18 x - 50 y = 191

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

9 x^{2} + 4 y^{2} - 72 x - 16 y + 124 = 0

What is 4x^2+16x+16y^2-32y-32=0 ?
The solution to 4x^2+16x+16y^2-32y-32=0 is Ellipse with (h,k)=(-2,1),a=4,b=2