y^2=9-4x^2

Solution

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

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

Solution steps

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

Rewrite

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

25 x^{2} + 16 y^{2} - 150 x + 64 y = 111

\frac{x ^{2}}{25} + \frac{y ^{2}}{1} = 1

\frac{x ^{2}}{2 7 ^{2}} + \frac{y ^{2}}{2 5 ^{2}} = 1

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

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

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