Does a biconvex lens have a shorter focal length than a plano-convex lens? Is there a ray-tracing diagram somewhere that shows precisely the difference between a Biconvex and Plano-convex lens?
 A: First. While asking this question, you should clarify the specific properties of the two lenses..
Let's say, their Radius of Curvature, optical density/refractive index and the medium in which they are put.
So as you have not mentioned any of these, I conclude that the radii of curvature is same for both lenses.
So now there can be two cases.
Case 1: Lenses are placed in a medium of less refractive index
So for a biconvex lens 
The focal length would be: 
1/f = (Π-1)(1/R -1/R).        { where Π = refractive index of lens/ refractive index of surrounding)
Putting the values you will get
f = R/2(Π--1)
And for a plano convex lens 
it will be.,.. f= R/(Π-1)
Now its clear that ::
focal length (plano convex) > focal length (biconvex)
Case 2: Lens putted in a refractive index greater that those of lens.
Then for bi convex f= R/2(Π-1)
and here Π-1 is negative..
For plano convex, f=R/(Π-1)
So both have -ve value and in this case as well
focal length (plano convex) > focal length (biconvex)
In magnitude, plano convex lens has always greater focal length than a bi convex lens.
A: The focal length can be designed to whatever you want for each type of lens. The difference comes into minimizing spherical aberration for your application. Typically, you would use a plano-convex lens for focusing a collimated beam, and a bi-convex lens for imaging (i.e. focusing diverging light). While either lens could be used in either case, this choice “spreads out” the curvature of the glass in such a way to reduce aberration. 
