What is (x-2)^2+4(y-3)^2=4 ?

The solution to (x-2)^2+4(y-3)^2=4 is Ellipse with (h,k)=(2,3),a=2,b=1

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(x-2)^2+4(y-3)^2=4

(x - 2)^{2} + 4 (y - 3)^{2} = 4

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

Solution steps

(x - 2)^{2} + 4 (y - 3)^{2} = 4

Rewrite

(x - 2)^{2} + 4 (y - 3)^{2} = 4

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

What is (x-2)^2+4(y-3)^2=4 ?
The solution to (x-2)^2+4(y-3)^2=4 is Ellipse with (h,k)=(2,3),a=2,b=1