y=x^2+y^2

Solution

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

(h, k) = (0, \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, \frac{1}{2}), a = \frac{1}{2}, b = \frac{1}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{1}{2}), b = \frac{1}{2}, a = \frac{1}{2}

18 x^{2} + 4 y^{2} - 72 x + 4 y + 37 = 0

9 (x - 1)^{2} + 4 y^{2} = 36

4 x^{2} + 9 y^{2} - 48 x + 72 y + 144 = 0

4 x^{2} + 2 y^{2} + 2 x - 8 y + 7 = 0

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

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