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

The solution to 5y^2+4x^2= 5/4 is Ellipse with (h,k)=(0,0),a=(sqrt(5))/4 ,b= 1/2

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5y^2+4x^2= 5/4

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

(h, k) = (0, 0), a = \frac{5}{4}, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{5}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{5}{4}, b = \frac{1}{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}{4}, b = \frac{1}{2}

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

\frac{( x - 4 ) ^{2}}{12} + \frac{( y + 3 ) ^{2}}{16} = 1

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

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

4 x^{2} - 40 x + 9 y^{2} + 54 y + 145 = 0

What is 5y^2+4x^2= 5/4 ?
The solution to 5y^2+4x^2= 5/4 is Ellipse with (h,k)=(0,0),a=(sqrt(5))/4 ,b= 1/2