Question

The graphs of the two linear equations $ax+by+c=0$ and $bx-ay=c$ are (are all not equal to zero)

• A. are parallel
• B. intersect at one point
• C. intersect at two points
• D. are perpendicular

Answer 1

Answer: (B), (D)

The correct options are
B intersect at one point
D are perpendicular

Let us find the slopes of the two lines $ax+by=c$ and $bx-ay=c$ with slopes $m_1=-\frac{a}{b}$ and $m_2=\frac{b}{a}$ respectively.

Now the product of the slopes gives:

$m_1\cdot m_2=(-\frac{a}{b})\left(\frac{b}{a}\right)=-1$

Therefore, the two lines are perpendicular.

Hence option D is correct.