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

The solution to y=4(x^2+y^2) is Ellipse with (h,k)=(0, 1/8),a= 1/8 ,b= 1/8

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

y = 4 (x^{2} + y^{2})

(h, k) = (0, \frac{1}{8}), a = \frac{1}{8}, b = \frac{1}{8}

Solution steps

y = 4 (x^{2} + y^{2})

Rewrite

y - 4 (x^{2} + y^{2}) = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{1}{8} ) ^{2}} + \frac{( y - \frac{1}{8} ) ^{2}}{( \frac{1}{8} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, \frac{1}{8}), a = \frac{1}{8}, b = \frac{1}{8}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, \frac{1}{8}), b = \frac{1}{8}, a = \frac{1}{8}

2 x^{2} + 2 y^{2} - 20 y = 0

4 x^{2} + 3 y^{2} + 8 x - 6 y - 41 = 0

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

49 x^{2} + 16 y^{2} + 196 x - 96 y = 444

\frac{x ^{2}}{16} + \frac{( y - 2 ) ^{2}}{25} = 1

What is y=4(x^2+y^2) ?
The solution to y=4(x^2+y^2) is Ellipse with (h,k)=(0, 1/8),a= 1/8 ,b= 1/8