Rest API client configuration in web.config C#

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C#

WCF

REST

API

I need to use Https mutual authentication in a rest API client since we only get the URI we can not add client certificate as we do for WCF.

What I have tried:

I have added keys in my web .config as below :
<appSettings>
    <add key="URI" value="https://localhost:8080/RestfulService/RestfulService.svc/restfulData" />
    <add key="CertificateValue" value="certficatename"/>
    <add key="CertificateLocation" value="LocalMachine"/>
    <add key="CertificateStoreName" value="My"/>
    <add key="CertificateFindType" value="FindBySubjectName"/>
</appSettings>

and I am using it in my API code as below:

X509Store store = new X509Store(ConfigurationManager.AppSettings["CertificateStoreName"], ConfigurationManager.AppSettings["CertificateLocation"]);
            store.Open(OpenFlags.ReadOnly);
            X509CertificateCollection certificates = store.Certificates.Find(ConfigurationManager.AppSettings["CertificateFindType"], ConfigurationManager.AppSettings["CertificateValue"], true);
            X509Certificate certificate = certificates[0];
            HttpWebRequest request = WebRequest.Create(requestUrl) as HttpWebRequest;
            request.ClientCertificates.Add(certificate);

HttpWebResponse response = request.GetResponse() as HttpWebResponse

Is this is the correct way to implement certificate authentication in Rest client or if not please help with the correct approach.