Does the curve $2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$ pass through $(0,0)$?












4












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Any ideas about why Desmos/Wolfram Alpha) does not show $(0,0)$ as a part of the curve $$2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$$ will be appreciated.



Am I missing something or is it a bug?






graphing-functions curves







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    4












    $begingroup$


    Any ideas about why Desmos/Wolfram Alpha) does not show $(0,0)$ as a part of the curve $$2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$$ will be appreciated.



    Am I missing something or is it a bug?






    graphing-functions curves







    share|cite|improve this question











    $endgroup$















      4












      4








      4





      $begingroup$


      Any ideas about why Desmos/Wolfram Alpha) does not show $(0,0)$ as a part of the curve $$2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$$ will be appreciated.



      Am I missing something or is it a bug?






      graphing-functions curves







      share|cite|improve this question











      $endgroup$




      Any ideas about why Desmos/Wolfram Alpha) does not show $(0,0)$ as a part of the curve $$2^2 x^2 + 4^2 y^2 = (x^2 + y^2)^2$$ will be appreciated.



      Am I missing something or is it a bug?






      graphing-functions curves




      graphing-functions curves






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Dec 15 '18 at 12:52









      amWhy

      1




      1










      asked Dec 15 '18 at 12:16









      Winged Blades of GodricWinged Blades of Godric

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          2 Answers
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          8












          $begingroup$

          Changing coordinates



          $$
          x = rcostheta\
          y=rsintheta
          $$



          we get



          $$
          r^2 (r^2 + 6 cos(2theta)-10) =0
          $$



          so clearly appear the two solutions



          $$
          r = 0\
          r^2 + 6 cos(2theta)-10=0
          $$



          enter image description here






          share|cite|improve this answer









          $endgroup$









          • 1




            $begingroup$
            This answer should be upvoted
            $endgroup$
            – Cloud JR
            Dec 15 '18 at 12:47



















          5












          $begingroup$

          Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.






          share|cite|improve this answer











          $endgroup$













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            2 Answers
            2






            active

            oldest

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            8












            $begingroup$

            Changing coordinates



            $$
            x = rcostheta\
            y=rsintheta
            $$



            we get



            $$
            r^2 (r^2 + 6 cos(2theta)-10) =0
            $$



            so clearly appear the two solutions



            $$
            r = 0\
            r^2 + 6 cos(2theta)-10=0
            $$



            enter image description here






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              This answer should be upvoted
              $endgroup$
              – Cloud JR
              Dec 15 '18 at 12:47
















            8












            $begingroup$

            Changing coordinates



            $$
            x = rcostheta\
            y=rsintheta
            $$



            we get



            $$
            r^2 (r^2 + 6 cos(2theta)-10) =0
            $$



            so clearly appear the two solutions



            $$
            r = 0\
            r^2 + 6 cos(2theta)-10=0
            $$



            enter image description here






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              This answer should be upvoted
              $endgroup$
              – Cloud JR
              Dec 15 '18 at 12:47














            8












            8








            8





            $begingroup$

            Changing coordinates



            $$
            x = rcostheta\
            y=rsintheta
            $$



            we get



            $$
            r^2 (r^2 + 6 cos(2theta)-10) =0
            $$



            so clearly appear the two solutions



            $$
            r = 0\
            r^2 + 6 cos(2theta)-10=0
            $$



            enter image description here






            share|cite|improve this answer









            $endgroup$



            Changing coordinates



            $$
            x = rcostheta\
            y=rsintheta
            $$



            we get



            $$
            r^2 (r^2 + 6 cos(2theta)-10) =0
            $$



            so clearly appear the two solutions



            $$
            r = 0\
            r^2 + 6 cos(2theta)-10=0
            $$



            enter image description here







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Dec 15 '18 at 12:38









            CesareoCesareo

            8,7693516




            8,7693516








            • 1




              $begingroup$
              This answer should be upvoted
              $endgroup$
              – Cloud JR
              Dec 15 '18 at 12:47














            • 1




              $begingroup$
              This answer should be upvoted
              $endgroup$
              – Cloud JR
              Dec 15 '18 at 12:47








            1




            1




            $begingroup$
            This answer should be upvoted
            $endgroup$
            – Cloud JR
            Dec 15 '18 at 12:47




            $begingroup$
            This answer should be upvoted
            $endgroup$
            – Cloud JR
            Dec 15 '18 at 12:47











            5












            $begingroup$

            Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.






            share|cite|improve this answer











            $endgroup$


















              5












              $begingroup$

              Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.






              share|cite|improve this answer











              $endgroup$
















                5












                5








                5





                $begingroup$

                Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.






                share|cite|improve this answer











                $endgroup$



                Not, it's not a bug. Yes, $(0,0)$ belongs to that curve, but it is an isolated point of the curve. In other words, no nearby point belongs to the curve. That's why you can't see it.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Dec 18 '18 at 14:25

























                answered Dec 15 '18 at 12:18









                José Carlos SantosJosé Carlos Santos

                160k22127232




                160k22127232






























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