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

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

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

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

(h, k) = (3, 2), a = 2, b = \frac{2}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (3, 2), a = 2, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, 2), a = 2, b = \frac{2}{3}

100 x^{2} + 9 y^{2} = 900

9 y^{2} + 16 x^{2} + 54 y - 64 x + 1 = 0

\frac{( x - 2 ) ^{2}}{49} + \frac{( y + 4 ) ^{2}}{16} = 1

25 x^{2} + 4 y^{2} - 225 = 0

16 x^{2} + 36 y^{2} - 224 x + 208 = 0

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