What is ((x-3)/2)^2+y^2= 9/4 ?

The solution to ((x-3)/2)^2+y^2= 9/4 is Ellipse with (h,k)=(3,0),a=3,b= 3/2

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((x-3)/2)^2+y^2= 9/4

(\frac{x - 3}{2})^{2} + y^{2} = \frac{9}{4}

(h, k) = (3, 0), a = 3, b = \frac{3}{2}

Solution steps

(\frac{x - 3}{2})^{2} + y^{2} = \frac{9}{4}

Rewrite

(\frac{x - 3}{2})^{2} + y^{2} = \frac{9}{4}

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{3 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 0), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 0), a = 3, b = \frac{3}{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{49} = 1

4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0

17 x^{2} + 16 y^{2} - 102 x - 32 y - 103 = 0

x^{2} - 4 x + 100 y^{2} + 200 y + 4 = 0

2 y - xx - yy > 0

What is ((x-3)/2)^2+y^2= 9/4 ?
The solution to ((x-3)/2)^2+y^2= 9/4 is Ellipse with (h,k)=(3,0),a=3,b= 3/2