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P and Q are two points of the hyperbola x^2/16 - y^2/25 =1 such that segment PQ subtends a right angle at the origin O.Show that 1/OP^2 +1/OQ^2 =(3/20)^2

P and Q are two points of the hyperbola x^2/16 - y^2/25 =1 such that segment PQ subtends a right angle at the origin O.Show that 1/OP^2 +1/OQ^2 =(3/20)^2

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1 Answers

vaibahv vardhan
31 Points
11 years ago

here we go by homogenisation , n we get an homogenous equation of the form ax2 + 2hxy + by2 = 0 , n we use a=b as it subtends a right angle at the origin. 

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