What is (2x-2)^2+(3y-6)^2=36 ?

The solution to (2x-2)^2+(3y-6)^2=36 is Ellipse with (h,k)=(1,2),a=3,b=2

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(2x-2)^2+(3y-6)^2=36

(2 x - 2)^{2} + (3 y - 6)^{2} = 36

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

Solution steps

(2 x - 2)^{2} + (3 y - 6)^{2} = 36

Rewrite

(2 x - 2)^{2} + (3 y - 6)^{2} = 36

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{x ^{2}}{12} + \frac{y ^{2}}{16} = 1

\frac{3}{2} u^{2} + \frac{1}{2} v^{2} = 4

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

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

x^{2} + 4 y^{2} = 20

What is (2x-2)^2+(3y-6)^2=36 ?
The solution to (2x-2)^2+(3y-6)^2=36 is Ellipse with (h,k)=(1,2),a=3,b=2