First slide

Equation of line in Straight lines

Question

For all real values of a and b $(2 a + b) x + (a + 3 b) y + (b - 3 a) = 0$ and $mx + 2 y + 6 = 0$ are concurrent, then m is equal to

Moderate

A

-2
B

-3
C

-4
D

-5

Solution

The given family of lines can be rewrite as    $a (2 x + y - 3) + b (x + 3 y + 1) = 0$
All these lines are passing through the point of intersection of    $2 x + y - 3 = 0, x + 3 y + 1 = 0$
Hence, the point of intersection of those two lines is    $(2, - 1)$
Since the line is $mx + 2 y + 6 = 0$ concurrent with the given family of lines, the line $mx + 2 y + 6 = 0$ passes through the fixed point    $(2, - 1)$
It implies that    $2 m - 2 + 6 = 0 \Rightarrow m = - 2$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App