What is X^2+Y^2-4Y<= 0 ?

The solution to X^2+Y^2-4Y<= 0 is Ellipse with (h,k)=(0,2),a=2,b=2

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X^2+Y^2-4Y<= 0

X^{2} + Y^{2} - 4 Y \leq 0

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

Solution steps

X^{2} + Y^{2} - 4 Y \leq 0

Rewrite

X^{2} + Y^{2} - 4 Y \leq 0

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{2 ^{2}} + \frac{( Y - 2 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{x ^{2}}{484} + \frac{y ^{2}}{289} = 1

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

(x - 2)^{2} + (2 y + 3)^{2} = 26

144 = 4 x^{2} + y^{2}

9 x^{2} + 18 x + 16 y^{2} - 64 y - 71 = 0

What is X^2+Y^2-4Y<= 0 ?
The solution to X^2+Y^2-4Y<= 0 is Ellipse with (h,k)=(0,2),a=2,b=2