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

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

Popular >

sqrt(x^2+y^2)=2*y/(sqrt(x^2+y^2))

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

(h, k) = (0, 1), a = 1, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 1, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 1, a = 1

16 x^{2} + 25 y^{2} - 64 x - 150 y - 11 = 0

36 (x^{2} - x) + 64 (y^{2} + 4 y) + 256 = 576

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{16} = 1

9 x^{2} + 25 y^{2} - 54 x - 100 y + 44 = 0

\frac{( x + 1 ) ^{2}}{8} + \frac{( y - \frac{3}{2} ) ^{2}}{4} = 1

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