Question

find locus of point P(x,y) such that x=t+1/t +1 and y=t- 1/t +2 where t is a parameter..

Answer 1

Answer:

(x - 1)² - (y - 2)² = 4

Step-by-step explanation:

Hi,

Given that x = t + 1/t + 1

x - 1 = t + 1/t

Squaring on  both sides, we get

(x - 1)² = t² + 1/t² + 2------(1)

Given that y - t = 1/t + 2

y - 2 = t - 1/t

Squaring on both sides, we get

(y - 2)² = t² + 1/t² - 2---------(2)

Subtracting (2) from (1), we get

(x - 1)² - (y - 2)² = 4 which is the locus .of the given point P(x, y)

It is a rectangular hyperbola.

Hope, it helps !