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What is the least distance between (0,12) and (a(t^2),2at) where a is constant and t is variable.
Let the distance between the given points be , then we know that Let, as when f(t) will be minimum and then D will also be minimum, , hence f’(t) is monotonically increasing. Minimum of f(t) is when f`(t) reaches zero. The answer thus depends on the value of and cannot be resolved easily in terms of a. So let us say that at t1 the value of f`(t) is zero and f(t) is minimum, right? Then, Hence, the expression doesn’t resolve to a constant value and the minimum distance will not have a uniform expression for different values of a.
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