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

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

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

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

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

Solution steps

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

Rewrite

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

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}

4 x^{2} + 9 y^{2} - 8 x - 54 y - 5 = 0

x^{2} + 4 y^{2} + 8 x + 8 y - 16 = 0

9 x^{2} + 16 y^{2} - 160 y + 256 = 0

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

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