4x^2+y^2=8

Solution

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

(h, k) = (0, 0), a = 2, b = 22

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 22, a = 2

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

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 2

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

3 = x^{2} + 9 y^{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{y ^{2}}{9} = 1

What is 4x^2+y^2=8 ?
The solution to 4x^2+y^2=8 is Ellipse with (h,k)=(0,0),a=sqrt(2),b=2sqrt(2)