# Equation of all lines passing through the intersection of lines #2x + 3y -5=0# and #x+y-2=0# is given by #(2x + 3y-5) + lambda(x+y-2) = 0#, of all these lines one line is farthest from point #(7,4)# the value of #lambda# is?

##### 1 Answer

#### Explanation:

Let us evaluate the coordinates of the point of intersection of the lines

and

The equations in s and y are:

and

Multiplying--2 by 2

Subtracting from ----1

or

--2 becomes

All the lines pass through the point

The point

Slope of this normal is

The slope of the line passing through

Slope of the line farthest from

The farthest line passes through the point

Slope of the farthest line is

Equation of the line is

Simplifying

Slope of the line

Here,

Slope,

Substituting for the slope of the line is

We have

ie