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

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

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4x^2+y^2=4x

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x - 1 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{6} + \frac{y ^{2}}{25} = 1

\frac{x ^{2}}{16} + \frac{y ^{2}}{81} = 1

x^{2} + y^{2} + 3 y = 0

\frac{x ^{2}}{16} + \frac{y ^{2}}{5} = 1

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