6=x^2+9y^2

Solution

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

(h, k) = (0, 0), a = 6, b = \frac{2}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 6 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 6, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 6, b = \frac{2}{3}

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

(3 x - 3)^{2} + (- 2 y - 4)^{2} = 43 + 9 + 16

36 x^{2} + 81 y^{2} = 49

49 x^{2} + 16 y^{2} - 784 = 0

9 x^{2} + 4 y^{2} - 54 x - 16 y + 61 = 0

What is 6=x^2+9y^2 ?
The solution to 6=x^2+9y^2 is Ellipse with (h,k)=(0,0),a=sqrt(6),b=sqrt(2/3)