JEE Main 2024 · Mathematics · Straight Lines and Circles · easy

The lines 2x+3y=5 and kx-6y=7 are perpendicular. The value of k is

Numerical answer

The lines

2x+3y=5

and

kx-6y=7

are perpendicular. The value of

k

Show answer and solution

Answer: 9

Two lines

a_1x+b_1y=c_1

and

a_2x+b_2y=c_2

are perpendicular when

a_1a_2+b_1b_2=0

. So

2k+3(-6)=0

, giving

k=9

. (Slopes:

-\tfrac23

and

\tfrac{k}{6}=\tfrac32

, product

-1

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