1. find the vertex of the parabola.

Question

4x=y^2+6y-11

2. find the center and radius of this circle
x^2+y^2-6x+4y-4=0

Answer 1

I will do the second question first

x^2+y^2-6x+4y-4=0
x^2 - 6x + ___ + y^2 + 4y + ___ = 4
x^2 - 6x + 9 + y^2 + 4y + 4 = 4 + 9 + 4
(x-3)^2 + (y+2)^2 = 17

centre is (3,-2) and radius is √17

by completing the square on the right side of the first equation, then dividing both sides by 4 gives you
x = .....

you must realize that this is a horizontal parabola, so be careful to read off the vertex.