The Locus Of Point Of Intersection Of Tangents At The Ends Of Normal Chord Of The Hyperbola x2 – y2 = a2 is

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Question

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola x2 – y2 = a2 is

Solution

Correct option is

 

Let P(hk) be the point of intersection of tangents at the ends of a normal chord of the hyperbola x2 – y2 = a2.

Then, the equation of the chord is  

      

But, it is a normal chord. So, its equation must be of the form  

      .

Equation (i) and (ii) represent the same line. 

     

  

  

Hence, the locus of P(hk) is a2(y2 – x2) = 4x2y2.

Testing

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