What is -8x^2-2y^2-12=0 ?

The solution to -8x^2-2y^2-12=0 is Ellipse with (h,k)=(0,0),a=sqrt(3/2),b=sqrt(6)

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-8x^2-2y^2-12=0

- 8 x^{2} - 2 y^{2} - 12 = 0

(h, k) = (0, 0), a = \frac{3}{2}, b = 6

Solution steps

- 8 x^{2} - 2 y^{2} - 12 = 0

Rewrite

- 8 x^{2} - 2 y^{2} - 12 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{3}{2}, b = 6

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 6, a = \frac{3}{2}

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

81 x^{2} + 64 y^{2} = 25

16 x^{2} + 9 y^{2} = 1

7 x^{2} + 16 y^{2} - 28 x + 128 y + 172 = 0

x^{2} - 16 x + 4 y^{2} - 12 y + 16 = 0

What is -8x^2-2y^2-12=0 ?
The solution to -8x^2-2y^2-12=0 is Ellipse with (h,k)=(0,0),a=sqrt(3/2),b=sqrt(6)