9=4x^2+y^2

Solution

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

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

Solution steps

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

Rewrite

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

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}}{9} + \frac{( y - 1 ) ^{2}}{36} = 1

\frac{- 6}{4} = \frac{x ^{2}}{1} + \frac{y ^{2}}{1}

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 2 ) ^{2}}{25} = 1

9 x^{2} + 25 y^{2} - 54 x + 100 y - 44 = 0

2 x^{2} - 8 x + y^{2} - 6 y + 7 = 0

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