x^2+4y^2=1

Solution

x^{2} + 4 y^{2} = 1

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

Solution steps

x^{2} + 4 y^{2} = 1

Rewrite

x^{2} + 4 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

\frac{x ^{2}}{25} + y^{2} = 1

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

\frac{x ^{2}}{16} + \frac{y ^{2}}{25} = 1

y > x^{2} - 3

\frac{x ^{2}}{36} - \frac{y ^{2}}{64} = 1

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