Question

Two particles start from the same point (2,-1) one moving 2 units along the line x+y=1 and the other 5 units along x-2y=4 if the particles move towards increasing y then their new position

Answer 1

Answer:

x = 2 - √2 ,  y = √2 - 1

x = 2(2 + √5)/√5  , (2 - √5)/√5

Step-by-step explanation:

Two particles start from the same point (2,-1) one moving 2 units along the line x+y=1 and the other 5 units along x-2y=4

particles move towards increasing y

x + y = 1

moving 2 units along the line x+y=1

(y -(1))² + (x - 2)² = 2²

=> (y + 1)² + (-y - 1)² = 4

=> 2(y + 1)² = 4

=> (y + 1)² = 2

=> y + 1 = √2   ( as Y is increaseing )

=> y = √2 - 1

& x = 2 - √2

x - 2y = 4

moving 5 units along the line x - 2y = 4

(y -(1))² + (x - 2)² = 2²

=> (y + 1)² + (2y + 2)² = 4

=>  (y + 1)² + 4(y + 1)² = 4

=> 5(y + 1)² = 4

=> (y + 1)² = 4/5

=> y + 1 = 2/√5   ( as Y is increaseing )

=> y = 2/√5  - 1  =   (2 - √5)/√5

& x = 2(2 + √5)/√5