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

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

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

y = \frac{x ^{2} + y ^{2}}{4}

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

Solution steps

y = \frac{x ^{2} + y ^{2}}{4}

Rewrite

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

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

2 x^{2} + y^{2} + 4 x - 6 y = 7

\frac{( x - 8 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{81} = 1

36 x^{2} + 9 y^{2} + 48 x - 36 y - 72 = 0

(x - 5)^{2} + (y - 1)^{2} + (y - 1)^{2} = 14

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