If origin and (3,2) are contained in the same angle of the lines 2x +y -a = 0 and x - Maths - Straight Lines

Question

If origin and (3,2) are contained in the same angle of the lines 2x
+y -a = 0 and x -3y +a=0 , then 'a' must lie in which interval?

Ajanta Trivedi · Accepted Answer

the given lines are L1(x,y)≡2x+y-a=0 (1) and L2(x,y)≡x-3y+a=0 (2) at (0,0) :L1(0,0)=-a and L2(0,0)=a at (3,2); L1(3,2)=2*3+2-a=8-a ;L2(3,2)≡3-3*2+a=-3+a now if origin and (3,2) are contained in the same angles, then L1(0,0) and L1(3,2) must have same sign andL2(0,0) and L2(3,2) must have same sign case I: if a>0 ⇒-a<08-a<0⇒a>8 and-3+a>0⇒a>3thus a∈(8,∞)caseII: if a<0 ⇒-a>08-a>0⇒a<8 and-3+a<0⇒a<3thus a∈(-∞,0) thus a must lie in the interval (-∞,0)∪(8,∞) hope this helps you

If origin and (3,2) are contained in the same angle of the lines 2x +y -a = 0 and x -3y +a=0 , then 'a' must lie in which interval?