First slide

Equation of line in Straight lines

Question

The locus of the moving point whose coordinates are given $by (e^{t} + e^{- t}, e^{t} - e^{- t}) where t is a parameter, is$

Easy

A

$x y = 1$
B

$x + y = 2$
C

$x^{2} - y^{2} = 4$
D

$x^{2} - y^{2} = 2$

Solution

$\begin{aligned} Let (e^{t} + e^{- t}, e^{t} - e^{- t}) \equiv (h, k) \\ or h = e^{t} + e^{- t} and k = e^{t} - e^{- t} \end{aligned}$
Squaring and subtracting, we get
$h^{2} - k^{2} = {(e^{t} + e^{- t})}^{2} - {(e^{t} - e^{- t})}^{2} = 4$
$Therefore, the locus of (h,k) is x^{2} - y^{2} = 4 .$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App