What is ((x-1)^2)/6+((y-3)^2)/2 =1 ?

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

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((x-1)^2)/6+((y-3)^2)/2 =1

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

(h, k) = (1, 3), a = 6, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 3), a = 6, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 3), a = 6, b = 2

\frac{12 ( x ) ^{2}}{24} + \frac{3 y ^{2}}{24} = \frac{24}{24}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{9} = 1

(y - 6)^{2} + 8 x^{2} = 64

x^{2} + 16 y^{2} - 128 y + 240 = 0

4 x^{2} + y^{2} = 6 y - 5

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