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

The foci 4x^2+y^2=4x is (1/2 ,(sqrt(3))/2),(1/2 ,-(sqrt(3))/2)

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foci 4x^2+y^2=4x

foci

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

(\frac{1}{2}, \frac{3}{2}), (\frac{1}{2}, - \frac{3}{2})

Solution steps

(h, k + c), (h, k - c)

Calculate ellipse properties

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

Ellipse with center

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

(\frac{1}{2}, 0 + c), (\frac{1}{2}, 0 - c)

Compute

c :

c = 1^{2} - (\frac{1}{2})^{2} : \frac{3}{2}

(\frac{1}{2}, 0 + \frac{3}{2}), (\frac{1}{2}, 0 - \frac{3}{2})

Refine

(\frac{1}{2}, \frac{3}{2}), (\frac{1}{2}, - \frac{3}{2})

9 x^{2} + 9 y^{2} + 18 x - 18 y + 14 = 0

\frac{x ^{2}}{81} + \frac{y ^{2}}{64} = 1

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

36 x^{2} + 9 y^{2} + 48 x - 36 y + 43 = 0

4 x^{2} + 9 y^{2} - 18 y - 27 = 0

What is the foci 4x^2+y^2=4x ?
The foci 4x^2+y^2=4x is (1/2 ,(sqrt(3))/2),(1/2 ,-(sqrt(3))/2)