Question 65149
The distance between the points (1,3) and (-2,7) is: 
d=sqrt((7-3)^2+(-2-1)^2)=sqrt(16+9)=5
---------------------------- 
Each of the remaining questions refer to the parabola y = 2x^2 + 12x + 17 
The vertex of the parabola is:
Vertex at x=-b/2a=-12/4=-3;y=2(3)^2+12(-3)+17=-1
Vertex at (-3,-1)
-------------------
The focus of the parabola is:
y-17+18 = 2(x^2+6x+9)
(x+3)^2=(1/2)(y+1)
4p=1/2
p=1/8
Focus at (-3,-1+(1/8))=(-3,-7/8)
-----------------
Thehe directrix of the parabola is: 
The horizontal line y = -9/8 
----------------
The length of the latus rectum of the parabola is: 
I think it is 4p=1/2
-----------
Cheers,
Stan H.