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

The solution to x^{(2)}-4x+3y^{(2)}=-2 is Ellipse with (h,k)=(2,0),a=sqrt(2),b=sqrt(2/3)

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

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

(h, k) = (2, 0), a = 2, b = \frac{2}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 2 ) ^{2}}{( 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (2, 0), 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) = (2, 0), a = 2, b = \frac{2}{3}

25 x^{(2)} + 4 y^{(2)} = 84

4 x^{2} - 16 x + 9 y^{2} + 54 y = - 61

(x^{2} + 9 x + 4 y^{2} + 10 y) = 14

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

9 x^{2} + 4 y^{2} - 12 x = 0

What is x^{(2)}-4x+3y^{(2)}=-2 ?
The solution to x^{(2)}-4x+3y^{(2)}=-2 is Ellipse with (h,k)=(2,0),a=sqrt(2),b=sqrt(2/3)