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

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

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2x^2+4y^2=5

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

9 x^{2} + 4 y^{2} \leq 36

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

\frac{x ^{2}}{36} + \frac{y ^{2}}{20} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{7} = 1

16 x^{2} + 9 y^{2} + 160 x - 72 y + 544 = 144

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