6=8x^2+y^2

Solution

6 = 8 x^{2} + y^{2}

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

Solution steps

6 = 8 x^{2} + y^{2}

Rewrite

6 = 8 x^{2} + y^{2}

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}

4 x^{2} + 7 y^{2} < 28

x^{2} + 9 y^{2} - 8 x + 36 y - 2 = 0

3 x^{2} + 9 x + y^{2} = 36 - (2 x^{2} + y^{2} - 3 x)

\frac{x ^{2}}{4} + \frac{y ^{2}}{25} - 1 \geq 0

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

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