If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =

We have three collinear points $\mathrm{A}(1,2) ; \mathrm{B}(-5,6) ; \mathrm{C}(a,-2)$.

In general if $\mathrm{A}\left(x_{1}, y_{1}\right) ; \mathrm{B}\left(x_{2}, y_{2}\right) ; \mathrm{C}\left(x_{3}, y_{3}\right)$ are collinear then,

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

So,

$1(6+2)-5(-2-2)+a(2-6)=0$

So,

$-4 a+8+20=0$

Therefore,

$a=7$

So the answer is (b)