If a and b are two arbitrary constants, then the straight li... | MATH - SLOPE OF LINE, EQUATION OF LINE IN | SolveeIt | Solveeit

Today, August 18

Question

If a and b are two arbitrary constants, then the straight line $( a - 2 b ) x + ( a + 3 b ) y + 3 a + 4 b = 0$ will pass through.

A

$( - 1 , - 2 )$

B

(1, 2)

C

$( - 2 , - 3 )$

D

(2, 3)

Answer

$( - 1 , - 2 )$

Explanation

Solution

$( a - 2 b ) x + ( a + 3 b ) y + 3 a + 4 b = 0$

or $a ( x + y + 3 ) + b ( - 2 x + 3 y + 4 ) = 0$ , which represents a family of straight lines through point of intersection of $x + y + 3 = 0$ and $- 2 x + 3 y + 4 = 0$ i.e, (– 1, – 2).

Trick : Point (–1, –2) satisfies the given equation of straight line.