What is 2y^2=4-5x^2 ?

The solution to 2y^2=4-5x^2 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(5)),b=sqrt(2)

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2y^2=4-5x^2

2 y^{2} = 4 - 5 x^{2}

(h, k) = (0, 0), a = \frac{2}{5}, b = 2

Solution steps

2 y^{2} = 4 - 5 x^{2}

Rewrite

2 y^{2} = 4 - 5 x^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{2}{5} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{2}{5}, 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}{5}

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{16} = 1

\frac{x ^{2}}{15} + \frac{y ^{2}}{64} = 1

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

28 x^{2} + 64 y^{2} - 84 x - 49 = 0

9 x^{2} + 4 y^{2} - 36 x - 24 y + 36 = 0

What is 2y^2=4-5x^2 ?
The solution to 2y^2=4-5x^2 is Ellipse with (h,k)=(0,0),a= 2/(sqrt(5)),b=sqrt(2)