Question

show that the points (at^2,2at),(a/t^2,-2a/t) and(a,0) are collinear for all values of a and t

Answer 1

this is the solution to the problem

Answer 2

points (at^2,2at),(a/t^2,-2a/t) and(a,0) are collinear  for all values of a and t

Step-by-step explanation:

points (at^2,2at),(a/t^2,-2a/t) and(a,0) are collinear

if area under these points = 0

=> (1/2) |  at²(-2a/t - 0)  + (a/t²)(0 - 2at)  + a(2at -(-2a/t) | = 0

=> (1/2) |  -2a²t  - 2a²/t  + 2a²t  + 2a²/t | = 0

=>  (1/2) |  0 | = 0

=> 0 = 0

hence points are collinear

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