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Question
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
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