Unattributed TMUA Mock Set A Paper 2 · Question 16

The real numbers $m$ and $c$ are such that the equation

x^2+(mx+c)^2=1

has a repeated root $x$ , and also the equation

(x-a)^2+(mx+c-1)^2=1

has a repeated root $x$ (which is not necessarily the same value of $x$ as the root of the first equation). $a$ is a real number. Which one of the following is a sufficient condition for there to be only 3 possibilities for the line $y=mx+c$ ?

a=\sqrt3

a>\sqrt3

a\ge\sqrt3

a<\sqrt3

a\le\sqrt3

examday

Unattributed TMUA Mock Set A Paper 2 · Q16