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Question
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Solution
Given that,
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Differentiating both the given parametric functions w.r.t. t
`"dx"/"dt" = 1 - 1/"t"^2`, `"dy"/"dt" = 1 + 1/"t"^2`
∴ `"dy"/"dx" = (("dy")/("dt"))/(("dx")/("dt"))`
= `(1 + 1/"t"^2)/(1 - 1/"t"^2)`
= `("t"^2 + 1)/("t"^2 - 1)`
Hence, `"dy"/"dx" = ("t"^2 + 1)/("t"^2 - 1)`.
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