Question

The value of a for which the lines $x=1$, $y=x$ and $a^{2}x+2ay-24=0$ are concurrent is:

• A. a = 4 or a = -6
• B. a = 4 or a = -4
• C. a = -4 or a = 6
• D. a = 6 or a = -6

Answer 1

The correct option is A a = 4 or a = -6

Since $x=1$, $y=x$ and $a^{2}x+2ay-24=0$ are concurrent
$\therefore$ Intersection of $x=1$ and $y=x$ lie on the line $a^{2}x+2ay-24=0$
$\Rightarrow$ $x=1$ and $y=1$ is a solution of given equation.
On substituting $x=1$ and $y=1$ in equation $a^{2}x+2ay-24=0$, we get
$\Rightarrow a^2\times 1+2\times ax-24=0\Rightarrow a^2\times 1+2\times a\times 1-24=0\Rightarrow a^2+2a-24=0$
$\Rightarrow (a+6)(a-4)=24$
$\Rightarrow a=4\text{or}a=-6$