x^2+5y^2=1

Solution

x^{2} + 5 y^{2} = 1

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

Solution steps

x^{2} + 5 y^{2} = 1

Rewrite

x^{2} + 5 y^{2} = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

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}{5}

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

x^{2} + 4 y^{2} - 4 x - 8 y - 92 = 0

\frac{x ^{2}}{5 ^{2}} + \frac{y ^{2}}{4 ^{2}} = 1

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

7 x^{2} + 16 y^{2} = 112

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