Find the equation of the two tangent lines to the ellipse $x^2+4y^2=36$ that pass through the point $(12,3)$.   I tried using implicit differentiation, and then I didn't know where to go from there.
I was solving a few problems from a textbook and I came across this one:     Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through   the point $P=(12,3)$   I could find the tangency points $$ but my solution was completely messy (I had four equations that I had to go back-and-forth with.  Is there an elegant/simple solution to that?  Tangency points:  $$P_1 = (0,3)$$ $$P_2 = \left( \frac{24}{5} , 3-\frac{24}{5} \right)$$
Can I get a rebate after using my HSA? How to create a color of the same brightness and saturation? Let's consider three colors: Red, Green and Blue. For blue I created a specific shade, something like #F2F5F7. If you see this color, it has a certain level of shade, brightness and saturation value of blue.  I want to create the same equivalent color but for Green and Red, how to get that? I have problems with getting an Asus PCE-N53 11n N600 PCI-E Adapter card to work on my desktop computer.  As far as I can tell no drivers are installed for the card. I know I can manually download the drivers directly from Asus, but I would rather not go that route.  If there are anyone that knows about any packages or other things I can do to make this work would be much appreciated.  Some systems details:  $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 12.04.1 LTS Release:    12.04 Codename:   precise   $ sudo lshw -C network   *-network                       description: Ethernet interface        product: RTL8111/8168B PCI Express Gigabit Ethernet controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:03:00.0        logical name: eth0        version: 06        serial: d4:3d:7e:03:b9:1d        size: 100Mbit/s        capacity: 1Gbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168e-3_0.0.4 03/27/12 ip=192.168.0.173 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s        resources: irq:43 ioport:d000(size=256) memory:f2104000-f2104fff memory:f2100000-f2103fff  *-network UNCLAIMED        description: Network controller        product: Ralink corp.        vendor: Ralink corp.        physical id: 0        bus info: pci@0000:04:00.0        version: 00        width: 32 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list        configuration: latency=0        resources: memory:f7100000-f710ffff  $ lsmod Module                  Size  Used by nvidia              12319264  51  vesafb                 13844  1  snd_hda_codec_hdmi     32474  1  joydev                 17693  0  bnep                   18281  2  rfcomm                 47604  0  bluetooth             180104  10 bnep,rfcomm snd_hda_codec_realtek   224173  1  snd_seq_midi           13324  0  ppdev                  17113  0  snd_rawmidi            30748  1 snd_seq_midi usbhid                 47199  0  hid                    99559  1 usbhid nouveau               774641  0  parport_pc             32866  1  snd_hda_intel          33773  5  ttm                    76949  1 nouveau snd_hda_codec         127706  3 snd_hda_codec_hdmi,snd_hda_codec_realtek,snd_hda_intel drm_kms_helper         46978  1 nouveau drm                   242038  3 nouveau,ttm,drm_kms_helper snd_seq_midi_event     14899  1 snd_seq_midi snd_hwdep              13668  1 snd_hda_codec snd_seq                61896  2 snd_seq_midi,snd_seq_midi_event i2c_algo_bit           13423  1 nouveau mxm_wmi                12979  1 nouveau wmi                    19256  1 mxm_wmi mac_hid                13253  0  snd_pcm                97188  3 snd_hda_codec_hdmi,snd_hda_intel,snd_hda_codec psmouse                97362  0  video                  19596  1 nouveau snd_timer              29990  2 snd_seq,snd_pcm snd_seq_device         14540  3 snd_seq_midi,snd_rawmidi,snd_seq snd                    78855  20 snd_hda_codec_hdmi,snd_hda_codec_realtek,snd_rawmidi,snd_hda_intel,snd_hda_codec,snd_hwdep,snd_seq,snd_pcm,snd_timer,snd_seq_device serio_raw              13211  0  soundcore              15091  1 snd snd_page_alloc         18529  2 snd_hda_intel,snd_pcm mei                    41616  0  lp                     17799  0  parport                46562  3 ppdev,parport_pc,lp r8169                  62099  0 Creating all possible line segments between all points using QGIS I want to connect all points in a point feature with every possible line segment using QGIS. For example, how a pentagon has five points with ten line segments connecting them all to form a pentagram inside. Alternatively phrased: How do I make spokes when all the points are hubs? I don't care about the order, I just want every connection between two points as one line each. Is there a tool or script that can do this in QGIS? This topic () is the closest to what I want but the plugins are no longer supported. My windows directory is huge I have always had problems with my windows directory's growing to a huge size.  It started with windows 95 then 98 then 2000 and xp.  Windows 7 however is absolutely huge.  The windows folder itself with out program files is 21.4 gigs...add the program files and other windows files and it is a whopping 32 gigs.  My question is why is it so large and what can I do about it.  At the rate this is going I will be out of space in now time. What are suitable TV sizes and viewing distances for couch surfing on a 1080p LCD HDTV? Use of Named Credentials seem to be tied to External Data Source Can a person residing in Singapore on a 5-month Employment Pass apply for a Schengen visa? System.JSONException: Malformed JSON: Expected '{' at the beginning of object I have getting the below JSON on using JSON.serialize  [ {   "lname" : "Singh",   "hcpZipCode" : null,   "hcpState" : null,   "hcpEmail" : "test@test.com",   "hcpCity" : null,   "hcpAddLine1" : null,   "fname" : "Abhey",   "countryCode" : "AUS" } ]   I don't know why this '[' is coming at the begining.I don't need this '[' at the begining due to which I am getting System.JSONException: Malformed JSON: Expected '{' at the beginning of object  code     public PageReference step2() {         string JSONstr='';        List&lt;HCPRequest&gt; conWrapList = new List&lt;HCPRequest&gt;();        HCPRequest tempcontactWrapper = new HCPRequest();        tempcontactWrapper.fname='Abhey';        tempcontactWrapper.lname='Singh';        tempcontactWrapper.countryCode='AUS';        tempcontactWrapper.hcpEmail=contact.Email;         conWrapList.add(tempcontactWrapper);          JSONstr = JSON.serializePretty(conWrapList);         System.debug('\n******'+JSONstr +'\n******');          String clientId = 'xy';         String clientSecret = 'x';          //We can also store our username password in custom setting.         String username='x';//salesforce username          String password='x';//password+securitytoken         // Generating the Access Token         HttpRequest req = new HttpRequest();         req.setMethod('POST');         req.setEndpoint('https://test.salesforce.com/services/oauth2/token');// this is the OAuth endpoint where this request will be hit         req.setBody('grant_type=password&amp;client_id='+clientId+'&amp;client_secret='+clientSecret+'&amp;username='+username+'&amp;password='+password);          Http http = new Http();         HTTPResponse res = http.send(req);         String str = res.getBody();         wrapObj = (Wrapper)Json.deserialize(str,Wrapper.class);         accessToken = wrapObj.access_token;         instanceUrl = wrapObj.instance_url;          HttpRequest req1 = new HttpRequest();         string response='';         req1.setMethod('POST');         //req.setEndpoint(wrapObj.instance_url+'/services/apexrest/Account/getAccountById?name=champaKAli');         string EndPt = 'y';         string email='test@test.com';         req1.setEndpoint(EndPt);         req1.setHeader('Authorization', 'OAuth '+wrapObj.access_token);          req1.setHeader('Content-Type', 'application/json');          //req1.setBody('{"request":{"lname" : "Singh","hcpZipCode" : null,"hcpState" : null,"hcpEmail" : "test@test.com","hcpCity" : null,"hcpAddLine1" : null,"fname" : "Abhey","countryCode" : "AUS"}}');          req1.setBody('{"request":'+JSON.Serialize(conWrapList)+'}');          //req.setBody('{"request": {"countryCode": "AUS","hcpEmail" : ""+email}}');          //req.setTimeout(60000);             //req.setHeader('Content-Length', '0');         Http http1 = new Http();         HTTPResponse res1 = http1.send(req1);          System.debug('***Response***** ' + res1.getBody());         if(res1.getBody()!=null)         {             response=res1.getBody();             HCPResponse saj=(HCPResponse)JSON.deserialize(response,HCPResponse.class);           System.debug('***Response came full***** ' + saj);            System.debug('***Response came***** ' + saj.accList);             for(HCPResponseDetail s :saj.accList)            {            System.debug('***Response email***** ' + s.hcpEmail);            System.debug('***Response add2***** ' + s.hcpAddrLine2);            contact.Address1_Line2__c=s.hcpAddrLine2;            }           //return response;         //string methodcall=methodGet(JSONstr);               return Page.opptyStep2CustomReg;         } Maximum Likelihood Estimation (MLE) in layman terms Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation. Error when using TikZ-Feynman package Today I downloaded and installed the new  package to draw Feynman diagrams. I included the packages   \usepackage{tikz}  \usepackage{tikz-feynman} \tikzfeynmanset{compat=1.0.0} \usetikzlibrary{shapes,arrows,positioning,automata,backgrounds,calc,er,patterns}   into my preamble (changed them already many times).  However, already a simple sample code like  \begin{tikzpicture} \begin{feynman} \vertex (a) {\(\mu^{-}\)}; \vertex [right=of a] (b); \vertex [above right=of b] (f1) {\(\nu_{\mu}\)}; \vertex [below right=of b] (c); \vertex [above right=of c] (f2) {\(\overline \nu_{e}\)}; \vertex [below right=of c] (f3) {\(e^{-}\)}; \diagram* { (a) -- [fermion] (b) -- [fermion] (f1), (b) -- [boson, edge label'=\(W^{-}\)] (c), (c) -- [anti fermion] (f2), (c) -- [fermion] (f3), }; \end{feynman} \end{tikzpicture}   directly gives the error:     Package pgfkeys Error: I do not know the key '/graph drawing/node distance'.   Can you please help me? Thanks in advance! I downvoted  and now really can't say why, so I wanted to remove my downvote. However, I get the message:  You last voted on this question yesterday Your vote is now locked in unless this question is edited  Why is this? I don't think I voted on it multiple times, and even when I did, I can change my mind, can't I? The most obvious answer everyone over the Internet is giving to this question is "Because anime is produced much faster compared to manga, they need to put in fillers in order to slow down the anime series". However, that shouldn't be the only reason.  For example, consider One Piece. The show is going on for more than 500 episodes, and less than 10% are fillers. Comparing that to Naruto, the show has almost the same number of episodes (original and Shippuuden combined), but almost 50% of its episodes are fillers. Needless to say, the manga of Naruto is so far ahead that the anime won't be able to catch up even if they produce 100+ episodes without any fillers. I'm trying to make a basic Windows application that builds a string out of user input and then adds it to the clipboard. How do I copy a string to the clipboard using Python? Proof that $1729$ is the smallest taxicab number I need to make Windows 7 STOP disabling the wifi adapter when the wired LAN is connected This is a Dell Latitude E6430. There is a setting in the bios to control this behavior and I have DISABLED it but it still happens. I am also running the latest bios.  When I plug in a network cable the wifi adapter becomes disabled. I need it to stay enabled. What else could be making this happen?  EDIT: The reason I need to do this is because with NETSH WLAN commands you can create a wifi hotspot by sharing the internet connection on the wired adapter and broadcasting a ssid on the virtual wifi nic. I do this all the time but it's not working on this laptop. I'm wondering if it's a network security thing where I am. I'm going to try from my hotel tonight and report back. Completely uninstall an app on Lollipop I am having a problem with uninstalling apps on Android 5.0 (Nexus 5). I am developing an Android app, so I debug/run the app directly on my device. For production, I exported the same app with my keystore, uninstalled the debug APK that I ran earlier, tried to install the signed APK, and I got this error:      An existing package by the same name with a conflicting signature is already installed.   Is it because the bytecodes are still in the ART runtime? Anyone has any idea how to solve this? As we all know, air consists of many gases including oxygen and carbon dioxide. I found that carbon dioxide is heavier than O2. Does the volume difference neglect the mass difference? Is it same for all other gases in air or is there another force that keeps all of these gases together?  If I take a breath of a fresh air, will the exhaled air be heavier because of its higher CO2 content? Will it fall on the floor? Weighting features prior to SVM I'm building an object detector using HOG features and linear SVM. 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