What is 8= 1/2 x^2+1/4 y^2 ?

The solution to 8= 1/2 x^2+1/4 y^2 is Ellipse with (h,k)=(0,0),a=4,b=4sqrt(2)

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8= 1/2 x^2+1/4 y^2

8 = \frac{1}{2} x^{2} + \frac{1}{4} y^{2}

(h, k) = (0, 0), a = 4, b = 42

Solution steps

8 = \frac{1}{2} x^{2} + \frac{1}{4} y^{2}

Rewrite

8 = \frac{1}{2} x^{2} + \frac{1}{4} y^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 0 ) ^{2}}{( 4 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 42

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 42, a = 4

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

x^{2} = 1 - 4 y^{2}

5 x^{2} + 9 y^{2} - 18 y - 36 = 0

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

4 x^{2} + 3 y^{2} + 8 x - 6 y = 5

What is 8= 1/2 x^2+1/4 y^2 ?
The solution to 8= 1/2 x^2+1/4 y^2 is Ellipse with (h,k)=(0,0),a=4,b=4sqrt(2)