Q. Prove that the distance between the points (at^2, 2at) and
is a/t^2, 2at/t) is a(t+1/t)^2
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2
Given points are A(at²,2at) , B(a/t²,-2a/t)
Calculate the distance between these points by using the distance formula.
S = √[(at²-a/t²)² + (2at+2a/t)²]
= √[a²(t²-1/t²)² + 4a²(t+1/t)²]
= √[a²(t⁴+1/t⁴-2) + 4a²(t²+1/t²+2)]
= a √(t⁴+1/t⁴-2+4t²+4/t²+8)
= a √ (t⁴+4t²+6+4/t²+1/t⁴)
= a √ (t + 1/t)⁴
= a √ [(t + 1/t)²]²
= a (t + 1/t)²
This is the required answer.
Answered by
1
√[(at²-a/t²)² + (2at+2a/t)²]
= √[a²(t²-1/t²)² + 4a²(t+1/t)²]
= √[a²(t⁴+1/t⁴-2) + 4a²(t²+1/t²+2)]
= a √(t⁴+1/t⁴-2+4t²+4/t²+8)
= a √ (t⁴+4t²+6+4/t²+1/t⁴)
= a √ (t + 1/t)⁴
= a √ [(t + 1/t)²]²
= a (t + 1/t)²
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