1)Write an equation for the parabola with focus (1,3)and vertex(0,3)

answer= x= 1/4(y-3)^2

2)Write an equation for a circle if the endpoints of a diameter are at (1,1)and(1,-9)
answer= (x-1)^2+(y+4)^2=25

3)Which is the equation of a circle with center (0,1)and radius 2 units?
answer= x^2+y^2-2y=4

1) correct for the vertex but I don't know about the focus

2) wrong ( I again plugged your equation into my calculator and I didn't get the diameter as what was given)

3) correct

what do you mean?

for number 2
A.(x-1)^2+(y+4)^2=5
C.(x+1)^2+(y-4)^2=5
D.(x+1)^2+(y-4)^2=25
is it A?

number 1
A.y=(x-4)^2-15
B.y=4(x-1)^2+5
C.y=4(x-1)^2-3

Checking again..2 is fine
I was looking on the wrong side of the circle for the diameter points.