A, B, C are Three Points On The Rectangular Hyperbola xy = c2, Find 1. The Area Of The Triangle ABC 2. The Area Of The Triangle Formed By The Tangents At A, B and C. 

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Question

 

ABC are three points on the rectangular hyperbola xy = c2, find

1. The area of the triangle ABC

2. The area of the triangle formed by the tangents at AB and C

Solution

Correct option is

 

Let coordinates of AB and C on the hyperbola xy = c2 are  respectively. 

1. Area of triangle ABC, 

       

       

       

       

2. equations of tangents at ABC are 

                  

            

  

  

where,  

              

  

From (i) 

       

       

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