Question

Number of real values of 'a' for which at least two of the straight lines given by $2x-ay=3,x+(a+a^2)y=1$ and $x-y=1$ are parallel , is

• A. $3$
• B. $4$
• C. $2$
• D. $0$

Answer 1

Answer: (A)

$3$

slope of equ. $ax+by=c$ is $\frac{-b}{a}$.

slope of equation $2x-ay=3$ is $\frac{a}{2},$ of $x+(a^2+a)y=1$ is $-(a+a^2)$

of $x-y=1$ is 1 . $\frac{a}{2}=1,-(a+a^2)=1,\frac{a}{2}=-(a+a^2)$

$\Rightarrow a\cdot 2,a=-2a-2a^2\Rightarrow a=0,-\frac{3}{2}$

$\therefore a^{2}2,0,\frac{-3}{2}$

i.e. 3 values.

So correct option is (A).