Question

find the equation of the straight line passing through the point of intersection of the lines 3x+2y+4=0,2x+5y=1 and whose distance from (2,-1) is 2?​

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+40λ−3=