What is 2X^2-6<-6Y^2 ?

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

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2X^2-6<-6Y^2

2 X^{2} - 6 < - 6 Y^{2}

(h, k) = (0, 0), a = 3, b = 1

Solution steps

2 X^{2} - 6 < - 6 Y^{2}

Rewrite

2 X^{2} - 6 < - 6 Y^{2}

in the form of the standard ellipse equation

\frac{( X - 0 ) ^{2}}{( 3 ) ^{2}} + \frac{( Y - 0 ) ^{2}}{1 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 3, b = 1

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

x^{2} + 4 y^{2} - 6 x - 55 = 0

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

(\frac{x - 2}{4})^{2} + (\frac{y + 3}{16})^{2} = 1

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