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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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