In the below MVC 6 appsettings.json file. 
Here is  two connections sting, one is default connection
"DefaultConnection" and send one
is "MVC6DemoContext".
You can see in below JSON file.
appsettings.json
{
  "ApplicationInsights": {
    "InstrumentationKey": ""
  },
  "Data": {
    "DefaultConnection": {
      "ConnectionString": "Server=(localdb)\\mssqllocaldb;Database=aspnet5-WebApplication1-b2a87fa4-3c62-4931-8248-76a6b22a08d1;Trusted_Connection=True;MultipleActiveResultSets=true"
    },
    "MVC6DemoContext": {
      "ConnectionString": "Server=myServer;Database=MVC6_Demo;User
ID=sa;Password=demo-password;
Trusted_Connection=True;MultipleActiveResultSets=true; Integrated
Security=false;"
    }
  },
  "Logging": {
    "IncludeScopes": false,
    "LogLevel": {
      "Default": "Verbose",
      "System": "Information",
      "Microsoft": "Information"
    }
  }
}
Configure
your connection string in application Start-up
  public class Startup
  {
        public Startup(IHostingEnvironment env)
        {
            // Set up configuration
sources.
            var builder = new ConfigurationBuilder()
                .AddJsonFile("appsettings.json")
                .AddJsonFile($"appsettings.{env.EnvironmentName}.json", optional: true);
            if
(env.IsDevelopment())
            {
                // For more details on using
the user secret store see http://go.microsoft.com/fwlink/?LinkID=532709
                builder.AddUserSecrets();
                // This will push telemetry
data through Application Insights pipeline faster, allowing you to view results
immediately.
               
builder.AddApplicationInsightsSettings(developerMode: true);
            }
            builder.AddEnvironmentVariables();
            Configuration = builder.Build();
        }
        public IConfigurationRoot Configuration { get; set; }
        // This method gets called by
the runtime. Use this method to add services to the container.
        public void ConfigureServices(IServiceCollection services)
        {
            // Add framework services.
           
services.AddApplicationInsightsTelemetry(Configuration);
            services.AddEntityFramework()
                .AddSqlServer()
                .AddDbContext<ApplicationDbContext>(options =>
                   
options.UseSqlServer(Configuration["Data:DefaultConnection:ConnectionString"]));
            services.AddEntityFramework()
                .AddSqlServer()
                .AddDbContext<DbContext>(options =>
                   
options.UseSqlServer(Configuration["Data:MVC6DemoContext:ConnectionString"]));
            services.AddIdentity<ApplicationUser, IdentityRole>()
                .AddEntityFrameworkStores<ApplicationDbContext>()
                .AddDefaultTokenProviders();
            services.AddMvc();
            // Add application services.
            services.AddTransient<IEmailSender, AuthMessageSender>();
            services.AddTransient<ISmsSender, AuthMessageSender>();
        }
        // This method gets called by
the runtime. Use this method to configure the HTTP request pipeline.
        public void Configure(IApplicationBuilder app, IHostingEnvironment env, ILoggerFactory loggerFactory)
        {
            loggerFactory.AddConsole(Configuration.GetSection("Logging"));
            loggerFactory.AddDebug();
           
app.UseApplicationInsightsRequestTelemetry();
            if
(env.IsDevelopment())
            {
                app.UseBrowserLink();
                app.UseDeveloperExceptionPage();
                app.UseDatabaseErrorPage();
            }
            else
            {
                app.UseExceptionHandler("/Home/Error");
                // For more details on
creating database during deployment see
http://go.microsoft.com/fwlink/?LinkID=615859
                try
                {
                    using (var serviceScope =
app.ApplicationServices.GetRequiredService<IServiceScopeFactory>()
                        .CreateScope())
                    {
                       
serviceScope.ServiceProvider.GetService<ApplicationDbContext>()
                            
.Database.Migrate();
                    }
                }
                catch { }
            }
            app.UseIISPlatformHandler(options
=> options.AuthenticationDescriptions.Clear());
           
app.UseApplicationInsightsExceptionTelemetry();
            app.UseStaticFiles();
            app.UseIdentity();
            // To configure external
authentication please see http://go.microsoft.com/fwlink/?LinkID=532715
            app.UseMvc(routes =>
            {
                routes.MapRoute(
                    name: "default",
                    template: "{controller=Home}/{action=Index}/{id?}");
            });
        }
        // Entry point for the
application.
        public static void Main(string[] args) => WebApplication.Run<Startup>(args);
   
}
For more detail, go to links