What is x^2+((y+3)/2)^2=4 ?

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

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x^2+((y+3)/2)^2=4

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

(h, k) = (0, - 3), a = 2, b = 4

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{2 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, - 3), a = 2, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 3), b = 4, a = 2

\frac{x ^{2}}{16} + \frac{y ^{2}}{12} = 1

y^{2} - x - 4 y + 3 = 0

x = 2 y^{2} - 4

(y - 33)^{2} = 4 a (x - h)

y^{2} + 4 x - 8 y + 12 = 0

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