Romeo and Juliet without Shakespeare!

Calculus Level 2

On a Chocolate Day , A Mathematician(Romeo) starts from his house which is located at point P(-3,4) and wants reach at His Girlfriend(Juliet) House which is located at point Q(0,1). But instantly he think that he Should buy chocolates for his Girlfriend(Juliet) to impress her. So He went to shop which is located at coordinate X-axis at point R(α\alpha .,0) .But he keep in mind that he should reach to his Girlfriend's House by travelling minimum distance otherwise She will be angry. As he is an Mathematician so he Chose a particular shop so that he reach His Girlfriend's House by travelling minimum Distance.Then find the value of α\alpha . so that he will impress his Girlfriend.

Let α\alpha =ab\frac { a }{ b }. Where 'a' and 'b' are coprime integers.

Then find the value of a×b\quad |a\times b|.


\bullet Assume that Mathematician is moving in Co-ordinate X-Y plane.

\bullet There are infinite number of Shops at Co-ordinate X-axis.So Mathematician(Romeo) choose Particular Shop To impress his Girlfriend(Juliet).

\bullet Treat all object as point object.

\bullet May be Fermat's Principle of Light waves Helpful Here .


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