I need to put this equation 4x2 + 9y2 - 8x + 36y + 4 = 0. In the standard ellipsis form.
Complete the square on the x and y terms...
$\displaystyle 4x^2 - 8x + 9y^2 + 36y + 4 = 0$
$\displaystyle 4(x^2 - 2x) + 9(y^2 + 4y) + 4 = 0$
$\displaystyle 4[x^2 - 2x + (-1)^2 - (-1)^2] + 9[y^2 + 4y + 2^2 - 2^2] + 4 = 0$
$\displaystyle 4[(x - 1)^2 - 1] + 9[(y + 2)^2 - 4] + 4 = 0$
$\displaystyle 4(x - 1)^2 - 4 + 9(y + 2)^2 - 36 + 4 = 0$
$\displaystyle 4(x - 1)^2 + 9(y + 2)^2 - 36 = 0$
$\displaystyle 4(x - 1)^2 + 9(y + 2)^2 = 36$
$\displaystyle \frac{(x - 1)^2}{9} + \frac{(y+2)^2}{4} = 1$.
Now I need to graph the Ellipsis whose equation is "4x2 + 9y2 - 8x + 36y + 4 = 0"
This means plotting, the Foci,center,length of major and minor axis, but none of this really makes sense to me..please help