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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

4 x^{2} - 40 x + 9 y^{2} + 54 y + 145 = 0

9 X^{2} + Y^{2} = 81

\frac{( x ^{2} - 2 x + 1 )}{34} + \frac{( y ^{2} - 8 y + 16 )}{25} = 1

y^{2} \leq - 4 x^{2} + 4

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