What is 3(x-1)^2+(y-3)^2=27 ?

The solution to 3(x-1)^2+(y-3)^2=27 is Ellipse with (h,k)=(1,3),a=3,b=3sqrt(3)

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3(x-1)^2+(y-3)^2=27

3 (x - 1)^{2} + (y - 3)^{2} = 27

(h, k) = (1, 3), a = 3, b = 33

Solution steps

3 (x - 1)^{2} + (y - 3)^{2} = 27

Rewrite

3 (x - 1)^{2} + (y - 3)^{2} = 27

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 3), a = 3, b = 33

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 3), b = 33, a = 3

4 x^{2} + y^{2} + 4 x + 2 y + 1 = 0

\frac{( x - 1 ) ^{2}}{64} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{1}{x + y i} + \frac{1}{x - y i} < - 1

6 x^{2} + 9 y^{2} = 54

53 x^{2} + y^{2} = 176

What is 3(x-1)^2+(y-3)^2=27 ?
The solution to 3(x-1)^2+(y-3)^2=27 is Ellipse with (h,k)=(1,3),a=3,b=3sqrt(3)