What is 4x^2+y^2=2y+3 ?

The solution to 4x^2+y^2=2y+3 is Ellipse with (h,k)=(0,1),a=1,b=2

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4x^2+y^2=2y+3

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

9 y^{2} + z^{2} = 16

\frac{x ^{2}}{2.8 9 ^{2}} + \frac{y ^{2}}{2.8 4 ^{2}} = 1

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

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{4} = 1

(\frac{y - ( - 2 )}{x - 3}) (\frac{y - 1}{x - ( - 2 )}) = - 6

What is 4x^2+y^2=2y+3 ?
The solution to 4x^2+y^2=2y+3 is Ellipse with (h,k)=(0,1),a=1,b=2