What is 3/2 u^2+1/2 v^2=4 ?

The solution to 3/2 u^2+1/2 v^2=4 is Ellipse with (h,k)=(0,0),a=(2sqrt(2))/(sqrt(3)),b=2sqrt(2)

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3/2 u^2+1/2 v^2=4

\frac{3}{2} u^{2} + \frac{1}{2} v^{2} = 4

(h, k) = (0, 0), a = \frac{2 2}{3}, b = 22

Solution steps

\frac{3}{2} u^{2} + \frac{1}{2} v^{2} = 4

Rewrite

\frac{3}{2} u^{2} + \frac{1}{2} v^{2} = 4

in the form of the standard ellipse equation

\frac{( u - 0 ) ^{2}}{( \frac{2 2}{3} ) ^{2}} + \frac{( v - 0 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore ellipse properties are:

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

4 x^{2} + 16 x + 5 y^{2} - 10 y + 1 = 0

\frac{x ^{2}}{4} + \frac{y ^{2}}{4} + \frac{x ^{2}}{9} = 1

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

8 x^{2} + z^{2} = 36

\frac{( x - 1.23 ) ^{2}}{1.4 1 ^{2}} + \frac{y ^{2}}{1.00 7 ^{2}} = 1

What is 3/2 u^2+1/2 v^2=4 ?
The solution to 3/2 u^2+1/2 v^2=4 is Ellipse with (h,k)=(0,0),a=(2sqrt(2))/(sqrt(3)),b=2sqrt(2)