You can get DbConnection
instance from DbContext
:
var context = new YourDbContext();
var connection = context.Database.Connection;
Of course, you can get connection string from connection, but you don't need thus you can use already existing connection object.
Here is Quick Watch of connection
object - as you can see it's simple ADO.NET SqlConnection object with ordinal connection string.
In config file I have Entity Framework connection string with metadata:
<connectionStrings>
<add name="NorthwindEntities"
connectionString="metadata=res://*/Northwind.csdl|res://*/Northwind.ssdl|res://*/Northwind.msl;provider=System.Data.SqlClient;provider connection string="data source=.;initial catalog=Northwind;integrated security=True;MultipleActiveResultSets=True;App=EntityFramework""
providerName="System.Data.EntityClient" />
</connectionStrings>