4x^2+y^2=9

Solution

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

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

2 x^{2} + 3 y^{2} + 12 x - 24 y + 60 = 0

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

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{5} = 1

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