What is 4x^2-16+y^2+2y=-1 ?

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

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4x^2-16+y^2+2y=-1

4 x^{2} - 16 + y^{2} + 2 y = - 1

(h, k) = (0, - 1), a = 2, b = 4

Solution steps

4 x^{2} - 16 + y^{2} + 2 y = - 1

Rewrite

4 x^{2} - 16 + y^{2} + 2 y = - 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 1), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 1), b = 4, a = 2

9 x^{2} + 49 y^{2} = 1

8 x^{2} + 18 y^{2} + 32 x - 36 y - 22 = 0

4 x^{2} + 2 y^{2} = 19

10 x^{2} + y^{2} - 40 x = 0

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

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