TMUA Official 2023 Paper 2 · Question 14

Three lines are given by the equations:

\begin{aligned}ax+by+c&=0\\bx+cy+a&=0\\cx+ay+b&=0\end{aligned}

where $a$ , $b$ and $c$ are non-zero real numbers.

Which one of the following is correct?

AIf two of the lines are parallel, then all three are parallel.

BIf two of the lines are parallel, then the third is perpendicular to the other two.

CIf two of the lines are parallel, then the third is parallel to

y=x

DIf two of the lines are parallel, then the third is perpendicular to

y=x

EIf two of the lines are perpendicular, then all three meet at a point.

FIf two of the lines are perpendicular, then the third is parallel to

y=x

GIf two of the lines are perpendicular, then the third is perpendicular to

y=x

examday