3=x^2+9y^2

Solution

3 = x^{2} + 9 y^{2}

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

Solution steps

3 = x^{2} + 9 y^{2}

Rewrite

3 = x^{2} + 9 y^{2}

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

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

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

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

9 x^{2} - 72 x + y^{2} + 10 y + 160 = 0

\frac{x ^{2}}{3} + \frac{y ^{2}}{6} = 1

What is 3=x^2+9y^2 ?
The solution to 3=x^2+9y^2 is Ellipse with (h,k)=(0,0),a=sqrt(3),b=sqrt(1/3)