How to find the vertex, focus, and directrix of an ellipse?

Question

I have the answer, but I need to know how to get the answers of:

x^2+4y^2-6x+20y-2=0

Answer 1

Find the vertices, foci, and directrices of an ellipse.
x² + 4y² - 6x + 20y - 2 = 0

Complete the square to put the equation into standard form.

x² + 4y² - 6x + 20y - 2 = 0
(x² - 6x) + (4y² + 20y) = 2
(x² - 6x + 9) + 4(y² + 5y + 25/4) = 2 + 9 + 25

(x - 3)² + 4(y + 5/2)² = 36
(x - 3)²/36 + (y + 5/2)²/9 = 1

The center of the ellipse (h,k) = (3, -5/2).

Semi-major axis
a² = 36
a = 6

Semi-minor axis
b² = 9
b = 3

c² = a² - b² = 36 - 9 = 27
c = √27 = 3√3

The foci are a distance c from the center of the ellipse in both directions along the major axis, which is horizontal. The foci are:

(h - c, k) and (h + c, k)
(3 - 3√3, -5/2) and (3 + 3√3, -5/2)

The vertices are a distance a from the center of the ellipse in both directions along the major axis, which is horizontal. The vertices are:

(h - a, k) and (h + a, k)
(3 - 6, -5/2) and (3 + 6, -5/2)
(-3, -5/2) and (9, -5/2)

The directrices are a distance a²/c in both directions from the center of the ellipse. They are lines perpendicular to the major axis with the equations:

x = h - a²/c = 3 - 36/(3√3) = 3 - 4√3
x = h + a²/c = 3 + 36/(3√3) = 3 + 4√3

Answer 2

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RE:
How to find the vertex, focus, and directrix of an ellipse?
I have the answer, but I need to know how to get the answers of:

x^2+4y^2-6x+20y-2=0

Answer 3

Directrix Of An Ellipse

Answer 4

you have to complete the square to get the equation into standard form. It helps to rewrite like this...

x^2 -6x + ____ + 4y^2 + 20y + ___ -2 = 0

complete the square for the x and y parts seperately. It will probably work out nice.