Application with no connection string - Where is the DB hidden? - database

Question

So, I have created a console application, added the entity framework nuget package, created a dbcontext and enabled migrations for my project.
However, I don't see the database anywhere. The database exists since I can query it when I run the application but since I haven't entered a connection string I don't see it anywhere in my SQL Management Studio.
My question is, where do Visual Studio "hide" this database?
Btw, I'm using EF6 Code First.
EDIT: Here is my app.config file:
<?xml version="1.0" encoding="utf-8"?>
<configuration>
<configSections>
<!-- For more information on Entity Framework configuration, visit http://go.microsoft.com/fwlink/?LinkID=237468 -->
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=6.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
</configSections>
<startup>
<supportedRuntime version="v4.0" sku=".NETFramework,Version=v4.5" />
</startup>
<entityFramework>
<defaultConnectionFactory type="System.Data.Entity.Infrastructure.LocalDbConnectionFactory, EntityFramework">
<parameters>
<parameter value="mssqllocaldb" />
</parameters>
</defaultConnectionFactory>
<providers>
<provider invariantName="System.Data.SqlClient" type="System.Data.Entity.SqlServer.SqlProviderServices, EntityFramework.SqlServer" />
</providers>
</entityFramework>
</configuration>

Answer 1

Add this to constructor of the context to see the default connection string used.
public class MyContext : DbContext
{
public MyContext()
{
Console.WriteLine(this.Database.Connection.ConnectionString);
}
}
Usually it creates the database in v11.0 or mssqllocaldb(in you app.config it is mssqllocaldb) instance of sqllocaldb.
The database file can be located at Users folder(Windows 8.1):
C:\Users\{UserName}\ApplicationName.ContextName.mdf