Question

a straight line L is drawn through th epoint A(2,1) such that its point of intersection with straight lines x+y=9 is at distance 3 root 2 from A find angle whch line lmakes with positive direction of x axis

Answer 1

Answer:

45°

Step-by-step explanation:

Let say Straight line drawn is

y = mx  + c

it passes through A (2 , 1)

=> 1 = 2m + c

=> c = 1 - 2m

=> y = mx + 1 - 2m

it intersect  x + y = 9

=> x + mx + 1 - 2m = 9

=> x (1 + m)  =  8 + 2m

=> x = (2m + 8)/(m + 1)

y = 9 - x  =  9 - (2m + 8)/(m + 1)

=> y = (7m + 1)/(m + 1)

((2m +8)/(m+1) - 2)²  + ((7m+1)/(m + 1) - 1)²  = (3√2)²

=> ( 6/(m+1))² + (6m/(m+1))² = 18

=> 36 + 36m²  = 18(m+1)²

=> 2 + 2m² = m² + 1 + 2m

=> m² - 2m + 1 = 0

=> (m - 1)² = 0

=> m = 1

=> Angle = 45° as Tan45° = 1

y = x + 1 - 2

=> y = x - 1