What is Y^2+2X^2-2Y+4X-6=0 ?

The solution to Y^2+2X^2-2Y+4X-6=0 is Ellipse with (h,k)=(1,-1),a=3,b= 3/(sqrt(2))

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Y^2+2X^2-2Y+4X-6=0

Y^{2} + 2 X^{2} - 2 Y + 4 X - 6 = 0

(h, k) = (1, - 1), a = 3, b = \frac{3}{2}

Solution steps

Y^{2} + 2 X^{2} - 2 Y + 4 X - 6 = 0

Rewrite

Y^{2} + 2 X^{2} - 2 Y + 4 X - 6 = 0

in the form of the standard ellipse equation

\frac{( Y - 1 ) ^{2}}{3 ^{2}} + \frac{( X - ( - 1 ) ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, - 1), a = 3, b = \frac{3}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), a = 3, b = \frac{3}{2}

8 x^{2} + 8 y^{2} + 16 y = 0

\frac{x ^{2} + 12 x + 36}{100} + \frac{y ^{2}}{64} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

1 = 4 x^{2} + 2 y^{2}

x^{2} + 2 y^{2} - 6 y = 18

What is Y^2+2X^2-2Y+4X-6=0 ?
The solution to Y^2+2X^2-2Y+4X-6=0 is Ellipse with (h,k)=(1,-1),a=3,b= 3/(sqrt(2))