How to render partial view in asp.net mvc

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MVC

partial-view

Hi I am using MVC Structure. I have to create a report which can be filtered by drop downs. I am thing to use a partial view to display report.
HEre is the structure of the page I want to achieve.
On top of page, there will be some drop down lists.
Below these will be page for report.

when user changes the options from dropdownlist, the report will be filtered.

I have two questions
1. How to render partial page.
2. How to refresh partial page through ajax/jquery. I want to do this on client side.

I have checked online, I am rendering page as shown in code below
**VIEW**

<h3>Report</h3>
<div>
    <table>
        <tr>
            <td>ServiceLine</td>
            <td>@Html.DropDownList("ServiceLine", null, new {id="ServiceLine"}) </td>
        </tr>
    </table>
</div>
<div>
    <h2>List</h2>
    <div>
        @Html.Partial("PartialView")
    </div>
</div>

This is what I have got in controller

public ActionResult PortfolioReport(char serviceLine)
{
    //Department List

     var serviceLines = Enum.GetValues(typeof(SogetiDepartments)).Cast<SogetiDepartments>().Select(v => new SelectListItem
    {
        Text = v.ToString(),
        Value = ((char)v).ToString(),
    });

     foreach (SelectListItem item in serviceLines)
     {
         if (Convert.ToChar(item.Value) == serviceLine)
             item.Selected = true;
     }


     ViewBag.ServiceLine = serviceLines;

    return View();
}

Any kind of help is appreciated.