Question

The line common to the two families of concurrent lines \[ x+y+\lambda(4x+3y-1)=0 \] and \[ 2x-3y+k(x+y-5)=0 \] is along the base of a triangle. If \((1,1)\) is the vertex of the triangle, then the perpendicular distance from that vertex to its base is

• A. \(\dfrac{1}{\sqrt5}\)
• B. \(\dfrac{3}{\sqrt7}\)
• C. \(\dfrac{4}{\sqrt{13}}\)
• D. \(\dfrac{9}{\sqrt{11}}\)

Hint:

For a family of concurrent lines \[ L_1+\lambda L_2=0, \] all the lines pass through the intersection of \[ L_1=0 \quad\text{and}\quad L_2=0. \] Find the common points of both families first, then determine the required line.

Answer 1

The Correct Option is C