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

\frac{x ^{2}}{49} + \frac{y ^{2}}{169} = 1

(- y - 6)^{2} + 8 x^{2} = 64

4 x^{2} + 24 x + 25 y^{2} + 200 y + 336 = 0

3 (x + 1)^{2} + (y - 1)^{2} = 6

\frac{x ^{2} + y ^{2} - x}{2 x - x ^{2} - y ^{2}} = 0

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