The locus of the moving point whose coordinates are given by `(e^t+e^(-t),e^t-e^(-t))` where `t` is a parameter, is `x y=1` (b) `x+y=2` `x^2-y^2=4` (d

Question

The locus of the moving point whose coordinates are given by `(e^t+e^(-t),e^t-e^(-t))` where `t` is a parameter, is `x y=1` (b) `x+y=2` `x^2-y^2=4` (d

The locus of the moving point whose coordinates are given by `(e^t+e^(-t),e^t-e^(-t))` where `t` is a parameter, is `x y=1` (b) `x+y=2` `x^2-y^2=4` (d) `x^2-y^2=2`
A. `xy=1`
B. `x+y=2`
C. `x^2-y^2=4`
D. `x^2-y^2=2`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
Let `(e^t+e^(-t),e^(t)-e^(-t))-=(h,k)`
or `h=e^t+e^(-t) and k=e^(t)-e^(-t)`
Squareing and subtracing we get
`h^2-k^2=(e^t+e^(-t))^2-(e^(t)-e^(-t))^2=4`
Therefore,the locus is `x^2-y^2=4`.

4 views Answered 2023-02-05 15:29