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

Sum

Solve the following.

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

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
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Chapter 3: Differentiation - Exercise 3.5 [Page 97]

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