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

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

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

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

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

Solution steps

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

Rewrite

(\frac{x - 1}{6})^{2} + \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{( x - 0 ) ^{2}}{20} + \frac{( y - 0 ) ^{2}}{36} = 1

2 x^{2} + 4 y^{2} = 200

3 x^{2} + 4 y^{2} = 1

\frac{( x - 3 ) ^{2}}{16} + \frac{( y - 1 ) ^{2}}{25} = 1

x^{2} + 4 y^{2} - 4 x - 12 = 0

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