9x^2+y^2=4

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x - 4 ) ^{2}}{9} + \frac{( y - 5 ) ^{2}}{4} = 1

- 8 y^{2} + 72 = 9 x^{2}

\frac{( x + 3 ) ^{2}}{36} + \frac{( y - 4 ) ^{2}}{16} = 1

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

10 - \frac{x ^{2}}{2} - y^{2} = x^{2} + 4 y^{2}

What is 9x^2+y^2=4 ?
The solution to 9x^2+y^2=4 is Ellipse with (h,k)=(0,0),a= 2/3 ,b=2