What is ((x+3)/2)^2+(y-2)^2= 1/4 ?

The solution to ((x+3)/2)^2+(y-2)^2= 1/4 is Ellipse with (h,k)=(-3,2),a=1,b= 1/2

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((x+3)/2)^2+(y-2)^2= 1/4

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

(h, k) = (- 3, 2), a = 1, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 3, 2), 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) = (- 3, 2), a = 1, b = \frac{1}{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{4} = 1

9 x^{2} + 5 y^{2} + 89 x - 60 y = 120

\frac{x ^{2}}{25} + \frac{y ^{2}}{81} = 1

\frac{x}{\frac{x ^{2}}{64} + \frac{y ^{2}}{9}} = 1

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

What is ((x+3)/2)^2+(y-2)^2= 1/4 ?
The solution to ((x+3)/2)^2+(y-2)^2= 1/4 is Ellipse with (h,k)=(-3,2),a=1,b= 1/2