What is ((y-3)^2)/9+((x-2)^2)/2 =1 ?

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

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((y-3)^2)/9+((x-2)^2)/2 =1

\frac{( y - 3 ) ^{2}}{9} + \frac{( x - 2 ) ^{2}}{2} = 1

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

Solution steps

\frac{( y - 3 ) ^{2}}{9} + \frac{( x - 2 ) ^{2}}{2} = 1

Rewrite

\frac{( y - 3 ) ^{2}}{9} + \frac{( x - 2 ) ^{2}}{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

4 X^{2} + 6 Y^{2} - 24 X + 2 Y - 12 = 0

25 y^{2} + 16 x^{2} + 50 y - 64 x - 311 = 0

25 x^{2} + 100 y^{2} = 400

4 x^{2} + 9 y^{2} - 8 x + 3 y + 4 = 0

\frac{( x - 2 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

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