Question

For all values of a and b the line $(a+2b)x+(a-b)y+(a+5b)=0$ passes through the point

• A. $(-1,2)$
• B. $(2,-1)$
• C. $(-2,1)$
• D. $(1,-2)$

Answer 1

The correct option is C $(-2,1)$

Given line

$(a+2b)x+(a-b)y+(a+5b)=0$

$ax+2bx+ay-by+a+5b$

$a(x+y+1)+b(2x-y+5)=0$

This will be possible

only if $x+y+1=0...\left(1\right)$

$2x-y+5=0...\left(2\right)$

$\left(1\right)+\left(2\right)\Rightarrow 3x+6=0$

$x=-2$

Substitute $x=-2$ in $\left(1\right)$

$-2+y+1=0$

$y=1$

$\therefore$ It always passes though point

$(-2,1)$