What is y^2=-6x^2+4 ?

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

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y^2=-6x^2+4

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 2 y^{2} + 2 x - 20 y = - 43

16 x^{2} + 16 y^{2} = 4 y^{2} + 20 y + 25

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

4 x^{2} + 8 y^{2} - 8 x + 48 y + 44 = 0

\frac{( ( x - 5 ) ^{2} )}{9} + \frac{( ( y - 4 ) ^{2} )}{36} = 1

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