x^2+3y^2=1

Solution

x^{2} + 3 y^{2} = 1

(h, k) = (0, 0), a = 1, b = \frac{1}{3}

Solution steps

x^{2} + 3 y^{2} = 1

Rewrite

x^{2} + 3 y^{2} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{1 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{1}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{1}{3}

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}{3}

x^{2} = 16 y

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

x^{2} + 24 x + y^{2} + 10 y = - 160

x^{2} = 4 y

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

What is x^2+3y^2=1 ?
The solution to x^2+3y^2=1 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(1/3)