x^2+4y^2=5

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

3 x^{2} + 4 y^{2} + 18 x + 8 y + 19 = 0

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

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

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

\frac{( x - 3 ) ^{2}}{4} + \frac{( y + 8 ) ^{2}}{16} = 1

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