What is ((y-2)^2+(x 1/2)^2)/9 =1 ?

The solution to ((y-2)^2+(x 1/2)^2)/9 =1 is Ellipse with (h,k)=(0,2),a=6,b=3

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((y-2)^2+(x 1/2)^2)/9 =1

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

(h, k) = (0, 2), a = 6, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{6 ^{2}} + \frac{( y - 2 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 6, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 6, b = 3

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

25 x^{(2)} + 4 y^{(2)} = 84

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

(x^{2} + 9 x + 4 y^{2} + 10 y) = 14

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

What is ((y-2)^2+(x 1/2)^2)/9 =1 ?
The solution to ((y-2)^2+(x 1/2)^2)/9 =1 is Ellipse with (h,k)=(0,2),a=6,b=3