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Answers
(2)
Given A≡ (t^2,2t) , B≡(1/t^2, -2/t), S≡(1,0).
We know that distance between the points (x1,y1) and (x2,y2) is given by
= > D = √(x2 - x1)^2 + (y2 - y1)^2.
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Now,
For SA, (x1,y1) = (1,0) and (x2,y2) = (t^2,2t).
Distance between the points SA = √(t^2 - 1)^2 + (2t - 0)^2
⇒ √t^4 + 1 - 2t^2 + 4t^2
⇒ √t^4 + 1 + 2t^2
⇒ √(t^2 + 1)^2
⇒ t^2 + 1.
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Now,
For SB, (x1,y1) = (1,0) and (x2,y2) = (1/t^2, -2/t)
Distance between the points SB = √(1/t - 1)^2 + (-2/t - 0)^2
⇒ √(1/t^2 + 1 + 2/t^2)
⇒ √(1/t + 1)^2
⇒ (1/t^2 + 1)
⇒ (1 + t^2)/t^2.
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Hence,
⇒ 1/SA + 1/SB
⇒ (1/t^2 + 1) + (t^2/t^2 + 1)
⇒ (1 + t^2)/(1 + t^2)
⇒ 1.
Hope it helps!