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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

(x - 2)^{2} + (y + 1)^{2} = 5 - 5 y^{2}

9 (x - 1)^{2} + (4 y)^{2} = 36

\frac{17 x ^{2} + 9 y ^{2} - 30 y + 9}{16} = 0

9 = \frac{1}{x ^{2} + y ^{2} - 7}

x^{2} + 8 y^{2} - 12 x - 16 y - 36 = 0

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