Solve the following. If x = a(1-1t),y=a(1+1t), then show that dydx=-1 - Mathematics and Statistics

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Sum

Solve the following.

If x = `"a"(1 - 1/"t"), "y" = "a"(1 + 1/"t")`, then show that `"dy"/"dx" = - 1`

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Solution

x = `"a"(1 - 1/"t")`

Differentiating both sides w.r.t. ‘t’, we get

`"dx"/"dt" = "a"[0 - ((-1)/"t"^2)] = "a"/"t"^2`

y = `"a"(1 + 1/"t")`

Differentiating both sides w.r.t. ‘t’, we get

`"dy"/"dt" = "a"[0 + ((-1)/"t"^2)] = "-a"/"t"^2`

∴ `"dy"/"dx" = (("dy"/"dt"))/(("dx"/"dt")) = ("-a"/"t"^2)/("a"/"t"^2)` = - 1

Concept: Derivatives of Parametric Functions
  Is there an error in this question or solution?
Chapter 3: Differentiation - Exercise 3.5 [Page 97]

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