Question

Please solve this question.

Answer 1

Given that twoo points P (at2,2at) and Q (a/t2,-2a/t) and S (a,0)
distance between two points = √((x2-x1)2 + (y2-y1)2)
distance between two points SP = √((a-at2)2 + (-2at)2 )
                                               ⇒  √( a2 [ (1-t2)2 + (4t2) ] )
                                               ⇒  √ (a2 (1+t2)2 )
                                              ⇒    a(1+t2)
distance between two points SQ = √((a-a/t2)2 + (2a/t)2 )
                                               ⇒  √( a2 [ (1-1/t2)2 + (41/t2) ] )
                                               ⇒  √ (a2 (1+1/t2)2 )
                                              ⇒    a(1+1/t2)
1 / SP + 1 / SQ = 1 / a(1+t2) + 1 / a(1+1/t2)
                        = (1+t2) / a(1+t2)
                        = 1 / a. (It is independent of t)
       

Answer 2

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