Question

A straight line produces equal but opposite points of intersection on two axes and passes through the intersection of two straight lines x + 3y + 4 = 0 and 2x - y = 13. Find the equation of the straight line.​

Answer 1

Step-by-step explanation:

Line passing through point of intersecting of L1,L2 is given by L1+λ2=0

⇒(3x+2y+4)+λ(2x+5y−1)=0

⇒x(3+2λ)+y(2+5λ)+4−λ=0

Distance of (2,−1) to this line,

∣∣∣∣∣∣(3+2λ)2+(2+5λ)22(3+2λ)−(2+5λ)+4−λ∣∣∣∣∣∣=2

⇒6+4λ−2−5λ=229λ2+32λ+13

⇒−2λ+8=229λ2+32λ+13

⇒λ2+16−8d=29λ2+32λ+13

⇒28λ2+

Answer 2

Answer

⇒y(−11)+11=0⇒ y=1