A line is drawn from to meet the lines and at points and

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A line

l

is drawn from

P(4,3)

to meet the lines

l_1:3x+4y+5=0

and

l_2:3x+4y+15=0

at points

A

and

B

, respectively. From

A

, a line perpendicular to

l

is drawn meeting

l_2

A_1

. Similarly, from

B

, a line perpendicular to

l

is drawn meeting

l_1

B_1

. Thus, a parallelogram

AA_1BB_1

is formed. Find the equation(s) of

l

so that the area of the parallelogram

AA_1BB_1

is least.