What is ((x-1)/2)^2+y^2= 1/4 ?

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

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((x-1)/2)^2+y^2= 1/4

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + 24 y^{2} = 100

- x^{2} - 2 y^{2} = - 40

9 x^{2} + 16 y^{2} - 36 x - 64 y + (- 44) = 0

(\frac{x - 4}{6})^{2} + (\frac{y + 2}{6})^{2} = 1

4 x^{2} + 9 y^{2} = 11

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