Question

If the coordinates of a variable point P be (t +1/t, t-1/t) where t is a variable quantity, then find the locus of 'P'.
(pls give some steps as well, don't just give final answer)
best ans will be BRAINLIEST​

Answer 1

let coordinate of variable point P be (x,y)

=> according to question,

x = t + 1/t , y = t - 1/t

=> square both sides ,

=> x² = t² + 1/t² + 2 => x² - 2 = t² + 1/t² ....... (1)

and y² = t² + 1/t² - 2 => y² + 2 = t² + 1/t²........(2)

(1) = (2)

=> x² - 2 = y² + 2

=> x² - y² = 4 ....... is the answer